50 0/5 pts 399 Emily is making a quilt and she has determined she needs 523 square inches of gray fabric and 1318 square inches of burgundy. How many square yards of each material will she need? Round your answers up to the nearest quarter yard. The gray fabric: square yards The burgundy fabric: square yards How many total yards of fabric will she have to buy? square yards

The value of x in the intersection point of the secant and tangent is 55°.

when a tangent and a secant intersect then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Therefore,

x = 1 / 2 (arc AED - arc DB )

Therefore,

arc AED  = 183°

arc DB = 73°

Therefore,

x = 1 / 2 (183 - 73)

x = 110 / 2

x = 55°

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Answer:

f(x)=(7x+9)(2x-5)

Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

Answer:

The volume is 40.96 cubic feet

Step-by-step explanation:

Given

\(V\ \alpha\ h * d^2\)

Where

\(V = Volume\\ h = height\\ d = distance\)

\(V = 15.84ft^3; h =22ft; d = 3ft\)

Required

The volume when h = 32 and d = 4

\(V\ \alpha\ h * d^2\)

Express as an equation

\(V = khd^2\)

Where k is the constant of variation.

Make k the subject

\(k = \frac{V}{hd^2}\)

Substitute \(V = 15.84ft^3; h =22ft; d = 3ft\)

\(k = \frac{15.84}{22 * 3^2}\)

\(k = \frac{15.84}{22 * 9}\)

\(k = \frac{15.84}{198}\)

\(k = 0.08\)

To solve for V when h = 32 and d = 4, we have:

\(V = khd^2\)

\(V = 0.08 * 32 * 4^2\)

\(V = 0.08 * 32 * 16\)

\(V = 40.96\)

The volume is 40.96 cubic feet

The volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is \(40.96 \: \rm ft^3\)

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

\(p = kq\)

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

\(p \propto q\)  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

\(m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}\)

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

\(m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}\)

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For this case, we have:
V = volume of the wood varying jointly as height of the tree and square of the distance around the trunk.

Let we take:

V will of course increase as r or h increases, and as it varies jointly, thus:

\(V \propto h r^2\)

Let  the constant of proportionality be 'k', then:

\(V = kr^2h\) (in cubic foot)

For case 1, it was specified that V = 15.84 cubic foot when r = 3 ft and h = 22 ft,

Putting these values gives us:

\(15.84 = k(3)^2(22)\\\\k = \dfrac{15.84}{198} = 0.08\)

Thus, we have:

\(\rm V = 0.08r^2 h \: \rm ft^3\)

Assuming second wood was also obtained from same kind of tree, we get the volume of the wood for h = 32 and r = 4 feet as:

\(V = 0.08 (4)^2 (32) = 40.96 \: \rm ft^3\)

Thus, the volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is \(40.96 \: \rm ft^3\)

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Answer:

Then we divide that amount by the original older value and get 1.3035. Now we must convert that number

Answer:

-30

Step-by-step explanation:

Multiply 5 by -6

Answer:

- 30 because

Step-by-step explanation:

5(-6) = -30/1 = -30

Spelled result in words is minus thirty.

How do you solve fractions step by step?

Multiple: 5 * (-6) = -30

Given:

Distance:   2      2.5    3    3.5    4

Time:        23      28    34   34   40

To find:

The scatter plot of the total time she exercises as a function of the distance she runs.

Solution:

Let y be the total time she exercise if she cover the distance x units..

From the given table, the ordered pairs are (2,23), (2.5,28), (3,34), (3.5,34) and (4,40).

Plot these points on a coordinate plane to get the scatter plot.

Now, the general equation of trend line is

\(y=mx+b\)

where, a is slope and b is y-intercept.

Using graphing calculator, we get the trend line and value of slope and y-intercept.

\(m=8, b=7.8\)

The equation of trend line is

\(y=8x+7.8\)

Therefore, the scatter plot of the total time she exercises as a function of the distance she runs is shown below and the equation of trend line is \(y=8x+7.8\).

Answer:

45

Step-by-step explanation:it gives you the answer chiices if you plug each number into x and then do the equation you will get 180

Answer:  45

Step-by-step explanation:

Did the test.

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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The equivalenet expression is 54\(n^{-11}\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

(\(6n^-5\))(\(3n^-3\))²

We can simplify as follows:

(\(6n^-5\))(\(9n^-6\))

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

\(n^-5 * n^-6 = n^-11\)

So the simplified expression is:

\(54n^-11\)

Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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Answer:

m ≤ 5

Step-by-step explanation:

I will begin by assuming m to be the number.

Then, the sum of m and 3 is: m + 3.

The symbol for "less than or equal to" is ≤.

So we form an inequality, like this :

m + 3 ≤ 8

To find m subtract 3 on each side:

m ≤ 5

Therefore, m ≤ 5.

Answer:

The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here). There is a lengthy reason, but the result is a slight modification of the Sector formula: Area of Segment = θ − sin(θ) 2 × r2 (when θ is in radians) Area of Segment = ( θ × π 360 − sin(θ)2 ) × r2 (when θ is in degrees)

2x+y=5 in slope intercept form

The slope intercept form is: y = mx +b, in other words, you just have to solve for "y"

2x+y=5

y = -2x + 5

Answer:

y = -2x + 5

In this form, the slope is -2 and the y-intercept is 5

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

Answer:

The mean and standard deviation changed to 23.5 and 14.62 respectively, based on all 12 samples.

Step-by-step explanation:

We are given that the Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.

Representing the data in tabular form;

           X                            \(X - \bar X\)                            \((X - \bar X)^{2}\)

          36                     36 - 20.5 = 15.5                   240.25

          14                      14 - 20.5 = -6.5                     42.25  

          21                       21 - 20.5 = 0.5                      0.25

          39                      39 - 20.5 = 18.5                   342.25

           11                        11 - 20.5 = -9.5                     90.25

           2                         2 - 20.5 = -18.5                  342.25    

        Total                                                                 1057.5      

Now, the mean of these value is given by;

        Mean, \(\bar X\)  =  \(\frac{\sum X}{n}\)

                         =  \(\frac{36+14+21+39+11+2}{6}\)

                         =  \(\frac{123}{6}\)  =  20.5

Standard deviation formula for discrete distribution is given by;

           Standard deviation, \(\sigma\)  =  \(\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }\)

                                                 =  \(\sqrt{\frac{1057.5 }{6-1} }\) = 14.54

Now, the manager has six more samples taken:

33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each

So, the modified table would be;

           X                            \(X - \bar X\)                            \((X - \bar X)^{2}\)

          36                     36 - 23.5 = 12.5                   156.25

          14                      14 - 23.5 = -9.5                     90.25  

          21                       21 - 23.5 = -2.5                     6.25

          39                      39 - 23.5 = 15.5                   240.25

           11                        11 - 23.5 = -12.5                   156.25

           2                         2 - 23.5 = -21.5                   462.25    

          33                       33 - 23.5 = 9.5                     90.25

         45                        45 - 23.5 = 21.5                   462.25

         34                        34 - 23.5 = 10.5                   110.25

          17                         17 - 23.5 = -6.5                    42.25

           1                           1 - 23.5 = -22.5                   506.25

          29                        29 - 23.5 = 5.5                   30.25      

        Total                                                                    2353      

Now, the mean of these value is given by;

        Mean, \(\bar X\)  =  \(\frac{\sum X}{n}\)

                         =  \(\frac{36+14+21+39+11+2+33+45+34+17+1+29}{12}\)

                         =  \(\frac{282}{12}\)  =  23.5

Standard deviation formula for discrete distribution is given by;

           Standard deviation, \(\sigma\)  =  \(\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }\)

                                                 =  \(\sqrt{\frac{2353 }{12-1} }\) = 14.62

The triangle in the image seems to be an isosceles triangle which means that two of the angles would be the same.

x would be 54° as well

to find the third angle, subtract all the angles from 180

\(180-54-54=72\)

y would be 72°

Answer:

270.47625

Step-by-step explanation:

249 is the original price

(249/100) · 8.625 = 21.47625 the tax total

249 + 21.47625 = 270.47625

Answer:

5.2x31 = 161.2

161.2+225=386.2

386.2+540=926.2

1000-926.2=73.8

73.8÷5.2=14.2

So, 14th August

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

Step-by-step explanation:

\( \cos( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } \\ = \sqrt{ \frac{1 - ( - \frac{15}{17}) }{2} } \\ = \sqrt{ \frac{32}{34} } \)

Answer:

The answer is B. But honestly tempeture rises with every layer.

a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

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Answer:

above is the answer to the question

Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

Check the picture below.

so the area of the pyramid is really just the summed up area of the 1.1x1.1 square on the base and four triangles with a base of 1.1 and a height of 2.4.

\(\stackrel{ \textit{\LARGE Areas} }{\stackrel{ square }{(1.1)(1.1)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{1.1})(\underset{h}{2.4}) \right]}}\implies 1.21+ 5.28\implies \text{\LARGE 6.49}~m^2\)

Answer:

Step-by-step explanation:

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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9514 1404 393

Answer:

  about 2.1

Step-by-step explanation:

The slope of the secant line is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (121/100 -1)/(11/10 -1) = (21/100)/(1/10) = 2.1

The slope of the tangent is about 2.1.

_____

Additional comment

We can refine our estimate by choosing a secant line between the points (9/10, 81/100) and (11/10, 121/100). That is, points either side of x=1.

That slope is ...

  (121/100 -81/100)/(11/10 -9/10) = (40/100)/(2/10) = 2.0

We expect the slope of the tangent at x=1 to be exactly 2.0.

Answer:

9?maybe

Step-by-step explanation:

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2