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The diameter of the lake is 6.2 m.

The diameter is the distance from one edge of the circle to the next across the center.

The diameter can be determined given the circumference and pi, since circumference is pi x diameter.

The number of times Gracie walks around the circular lake = 15 times

The total distance covered by the walk = 2,178 meters

The circumference (the distance around the edge of the circular lake) is 145.2 m (2,178 ÷ 15).

Circumference = C = 2πr = πd

Diameter = C/π

145.2  ÷ 3.143

= 46.2 m

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The measure of the angle ADC is: 20°

The parameters are given as:

∠ABC = 40°

∠ADC = ?

We know from circle geometry that:

Angle subtended at the center is twice the angle subtended at the circumference.

Therefore:

∠ABC = 2 x ∠ADC

On substituting the value we get:

40° = 2 * ∠ADC

∠ADC = 20°

Therefore, the measure of the angle ADC is 20°

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Complete question is:

A circle is centered on point B. Points A, C and D lie on it's circumference.

If ABC measures 40 degrees, what does ADC measure?

The coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

A triangle is a closed, two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and can be formed by connecting three non-collinear points. Triangles can be classified based on their side lengths and angles.

To solve this problem, we can use the fact that the area of a triangle is equal to half the product of its base and height. Let's first find the length of the sides of the square.

Since the area of the square is 1320 square centimeters, we can find its side length by taking the square root of 1320:

√(1320) ≈ 36.32

So the side length of the square is approximately 36.32 cm.

Next, let's find the coordinates of points E and F. Since E is the midpoint of AB, its coordinates are:

E = ((0+36)/2, (36+0)/2) = (18, 18)

Similarly, since F is a quarter point of BC close to point B, its coordinates are:

F = (36, (3/4)36) = (36, 27)

Now let's find the equation of line CE. Since we know two points on the line (C and E), we can use the point-slope form of a linear equation to find its equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line. We can find the slope of the line by taking the difference in y-coordinates and dividing by the difference in x-coordinates:

m = (0 - 36)/(36 - 18) = -2

Using the point-slope form with point C, we get:

y - 0 = -2(x - 36)

y = -2x + 72

Similarly, the equation of line DB can be found using points D and B:

m = (0 - 36)/(0 - 18) = 2

y - 0 = 2(x - 0)

y = 2x

Finally, we can find the coordinates of point P by solving the system of equations:

y = -2x + 72

y = 2x

Setting the two expressions for y equal to each other, we get:

-2x + 72 = 2x

4x = 72

x = 18

Substituting x = 18 into either equation, we get:

y = 2x = 36

So the coordinates of point P are (18, 36). To find the coordinates of point Q, we can use the fact that it lies on line DF. Since we know two points on the line (D and F), we can again use the point-slope form of a linear equation:

m = (27 - 0)/(36 - 0) = 3/4

y - 0 = (3/4)(x - 0)

y = (3/4)x

To find the intersection point of lines DF and CE, we need to solve the system of equations:

y = (3/4)x

y = -2x + 72

Setting the two expressions for y equal to each other, we get:

(3/4)x = -2x + 72

(11/4)x = 72

x = 64/11

Substituting x = 64/11 into either equation, we get:

y = (3/4)(64/11) ≈ 14.73

So the coordinates of point Q are (64/11, 14.73).

Hence, Now that we have the coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

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The numbers are characterized as rational and irrational numbers as below

1. 3.2 x 10³ - R (Rational)

2. 4/3 - R (Rational)

3. 1.423... - I (Irrational)

4. TT/6 - I (Irrational)

Rational numbers harmonized with a fraction of two integers where the denominator must not be zero. In simpler terms, it can be conveyed as p/q whereby both "p" and "q" are integers while "q" is unequal to zero.

As opposed to rational numbers, irrational ones cannot be expressed in a fraction or quotient of two integers. It's not possible to write them down in terms of the figure p/q whereby "p" and "q" are integers, differing from one another, and "q" is also inequivalent to zero.

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[tex]x^2-5x+22=7x+2\implies x^2-12x+20=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-12}x\stackrel{\stackrel{c}{\downarrow }}{+20}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-12)^2-4(1)(20)\implies 144-80\implies 64[/tex]

The retail selling price of the keyboard is $43.75.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

To find the retail selling price of the keyboard, we need to add the markup to the cost of the keyboard.

The markup of 150% means that the retailer is adding 150% of the cost to the selling price.

To calculate this, we can first find the dollar amount of the markup:

Markup = 150% of $25

Markup = 0.5 * 150 * $25

Markup = $18.75

This means that the retailer is adding $18.75 to the cost of the keyboard to get the selling price. To find the selling price, we can add the markup to the cost:

Selling price = Cost + Markup

Selling price = $25 + $18.75

Selling price = $43.75

Therefore, the retail selling price of the keyboard is $43.75.

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Step-by-step explanation:

5x² - 19x - 4

use the discriminant formula

D = b² - 4ac

label the coefficients

5 = a -19 = b -4 = c

D = -19² - 4(5)(-4)

D = -281

since the discriminant is negative this eqaution ahs no real solutions

The curve is defined as follows

A. absolute minima

B. absolute maxima

C. neither

D. relative minima

E. relative maxima

F. neither

G.  neither

When examining a function, its absolute minimum refers to the lowest possible value it can reach throughout its entire domain.

In a similar manner, absolute maximum pertains to the highest value that said function is capable of attaining within the same specified range, without consideration of separate intervals or regions.

To reiterate, these values denote the smallest and largest outcomes the function can yield over its complete set of input values, regardless of where those values may be located.

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Answer: 4/5

Step-by-step explanation: In decimal form: 0.8

The length of the arc of the circle that has a radius of 16 inches and a central angle of 75 degrees is calculated as 6.66π inches (to two decimal places).

The length of an arc is calculated using the formula below:

arc length = θ/360 * 2 * π * r

Given the variables:

Central angle (θ) = 75 degrees

radius (r) = 16 inches

Plug in the values:

arc length = 75/360 * 2 * π * 16

length of arc ≈ 6.66π inches (to two decimal places).

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Answer: E

Step-by-step explanation:

Put each function into the slope-intercept form y=mx+b. Notice that m=1 for each function, and because m represents the slope, all slopes are the same.

Answer: 5.1%

Step-by-step explanation:

The formula for calculating the effective annual yield when the interest is compounded semiannually is given by:

(1 + (r/n))^n - 1

where r is the annual interest rate and n is the number of times the interest is compounded in a year.

In this case, r = 5% and n = 2 (since the interest is compounded semiannually). Substituting these values into the formula, we get:

(1 + (0.05/2))^2 - 1

= (1.025)^2 - 1

= 1.050625 - 1

= 0.050625

Multiplying this value by 100 gives the effective annual yield as a percentage:

0.050625 x 100 = 5.0625%

Rounding this to the nearest tenth of a percent, we get:

Effective annual yield = 5.1%

Therefore, the effective annual yield for the given savings account, rounded to the nearest tenth of a percent, is 5.1%.

Answer: Angle aeb

Step-by-step explanation: To be supplementary, the angle(s) must add up to 180. Angle AEB and angle DEA add to 180. Another way to find this is to find the angle that the angle is adjacent to in a straight line.

Answer:

  x+3 . . . . if x > 5

Step-by-step explanation:

You want the meaning of |x+3| if x > 5.

The absolute value function is a piecewise defined function:

  [tex]y=|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]

The expression (x+3) is zero when x=-3. So, your absolute value function will have the piecewise definition ...

  [tex]|x+3|=\begin{cases}-(x+3)&\text{for }x < -3\\x+3&\text{for }x\ge-3\end{cases}[/tex]

You are interested in the value for x > 5, which is definitely greater than -3. That means only the second part of this definition is applicable.

  x+3 . . . . if x > 5

__

Additional comment

The attache graph shows the given absolute value expression (dashed red line). The blue line is (x+3) for x > 5. You can see that it matches the given expression in that region.

After using synthetic division, the answer are given as follows;

first row          = -4, 4, 12

Second Row = -2 2 -6 -5

Answer = 6 + [-5/x-2]

-2x^3+6x^2-10x+7 / x-2

Coefficient of the numerator polynomial are:

- 2, 6, -10 , 7

the zeros of the denominator are:

x -2 = 0
x = 2

              X³       X³    X¹     X⁰
               -2        6     -10    7

2                                                  

      X³       X³    X¹     X⁰
               -2        6     -10    7

2               ↓        -4        4   -12                

                 -2        2     -6     -5

So the quotient is -2x² +2x - 6 remainder -5

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The linear equations from the options given are expressed as: y = 5 and y = -2/5x + 4.

An equation is linear can be expressed in the following forms:

y = mx + b

x = b

y = b

In the above, y is the dependent variable and x is the independent variable, m = slope, and b = y-intercept.

Note that in a linear equation the exponent of the variable is always 1. On the other hand, a nonlinear equation has an exponent that is not equal to 1 and can be expressed as:

y = x²

Therefore, the equations that are linear are:

y = 5 and y = -2/5x + 4.

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Answer:To evaluate the function for f(2), we simply substitute x = 2 into the function

:f(2) = 8(2) + 7

Simplifying the expression:

f(2) = 16 + 7f(2) = 23

Therefore, f(2) = 23.

Step-by-step explanation:

Answer: 1204 cm²

Step-by-step explanation:

The upper bound of the area of a page would be the area of a rectangle with the upper bound of the length and width measurements.

Given that each page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest centimetre, the upper bound of the length would be 43.5 cm (since we round up to the nearest centimetre) and the upper bound of the width would be 28.5 cm.

Therefore, the upper bound of the area of a page would be:

43.5 cm x 28.5 cm = 1240.25 cm²

Rounding this value to the nearest whole number, we get:

1204 cm²

So, the upper bound of the area of a page is 1204 cm².

Answer:

1204 cm 2

Step-by-step explanation:

Answer:

We can use the formula:

average speed = total distance / total time

To find the total distance, we add the distances for each event:

total distance = 1.5 km (swimming) + 40 km (cycling) + 1 km (running) = 42.5 km

To find the total time, we add the times for each event:

time for swimming = distance / speed = 1.5 km / 2.5 km/h = 0.6 hours

time for cycling = 40 km / 12 km/h = 3.33 hours

time for running = 1 km / 9 km/h = 0.11 hours

total time = 0.6 hours + 3.33 hours + 0.11 hours = 4.04 hours

Now we can calculate the average speed:

average speed = total distance / total time = 42.5 km / 4.04 hours ≈ 10.52 km/h

Therefore, Farhan's average speed for the entire competition is approximately 10.52 km/h.

Answer:

!

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, - 6) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m = [tex]\frac{0-(-6)}{6-(-6)}[/tex]= [tex]\frac{0+6}{6+6}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

The lower quartile corresponds to the 25th percentile of the data set. To find the maximum value for the lower quartile, we need to find the largest number that is at or below the 25th percentile.

The range of the numbers that the random number generator can pick is 69 - 7 + 1 = 63. The 25th percentile corresponds to the value that is 25% of the way through this range, which is:

0.25 * 63 = 15.75

Since we can't pick a fractional number, we need to round down to 15. Therefore, the maximum value for the lower quartile is 15.

Statement of Cash Flows (Indirect Method)

For the 3 months ended March 31, 2020

Angel Company

Net income $64,018

Adjustments to reconcile net income to net cash provided by

operating activities:

Depreciation 1,250 Depreciation

Equity method earnings from Titan investment (5,880) Equity investment earnings

Increase in value of marketable investments (100) Allowance for decrease in value

Deferred taxes payable 336 Deferred taxes

Gain on sale of marketable investments (2,400) Gain on sale of marketable investments

Changes in assets and liabilities:

Accounts receivable (25,000) Accounts receivable

Inventory (17,500) Inventory

Accounts payable 17,197 Accounts payable

Income taxes payable 13,529 Income taxes payable

Other assets - -

Bonds payable 65,000 Bonds payable

Net cash provided by operating activities $44,570

Investing activities:

Proceeds from sale of marketable securities $11,400 Proceeds from sale of securities

Proceeds from condemnation award 29,860 Condemnation award proceeds

Purchase of equipment (81,500) Equipment purchases

Net cash used in investing activities (40,240)

Financing activities:

Issuance of bonds payable $65,000 Bond issuance

Dividends paid (8,000) Dividends paid

Issuance of common stock 30,000 Common stock issuance

Net cash provided by financing activities 87,000

Net increase in cash $91,330

Cash at beginning of period 25,300 Cash, beginning of period

Cash at end of period $116,630 Cash, end of period

Answer:

c c c c c c c c c c c c c c c c c c c c c c c c c c c c c

The probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.

what is probability?

In general terms, probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty or randomness in various situations.

In formal terms, probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in an event. It is usually represented as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an adult being willing to change their diet can be calculated using the given information as follows:

Probability of an adult being willing to change diet = Number of adults willing to change / Total number of adults

Total number of adults = 400 (as given in the question)

Number of adults willing to change = 116 (as given in the question)

Therefore, the probability of an adult being willing to change their diet can be calculated as:

Probability = 116/400

Probability = 0.29 or 29%

So, the probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.

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Answer:b 40

A60

Step-by-step explanation:

Answer:

Step-by-step explanation:

so for figure a:

we can find x by using sin which is sin = opposite/hypotenuse so

- sin30= x/10cm(sin30 is equivalent to 1/2 or 0.5)

- 0.5= x/10cm or 1/2=x/10cm (i'm gonna use the 2nd option)

- 10cm * 1/2=x

-x=5cm

and for figure b:

here we also use sin

- sin 50= x/8cm (sin 50 is equivalent to 0.7660 )

- 0.7660= x/ 8cm

-0.7660 * 8cm=x

- x= 6.128cm and when estimated x= 6cm

Answer: In that picture the slope is increasing

Step-by-step explanation: positive rise and positive run (uphill from left to right)

Answer:

83 degrees

Step-by-step explanation:

See attachment below: