Petra is making a batch of extra large donuts by stamping circles in dough using a pastry stamp with a diameter of 5 inches. For the donut hole, she stamps out a circle using a pastry stamp that has a diameter of 2 inches.

How many square inches of dough are left in the donut after the hole has been removed?

Using the Law of Cosines, the angle between the lines PX and PY is found to be approximately 101.5°. Subtracting this angle from the bearing of Y from P (125°) and the bearing of X from P (35°) gives a bearing of approximately 54.5° from X to Y.

We can use the Law of Cosines to find the angle between the lines PX and PY, and then add this angle to the bearing of X from P to find the bearing of Y from X.

Let A be the angle between the lines PX and PY, and let C be the distance between X and Y. Then we have

C² = PX² + PY² - 2(PX)(PY)cos(A)

Substituting the given values, we get

950² = 420² + PY² - 2(420)(PY)cos(A)

Solving for cos(A), we get

cos(A) = (PY^2 - 950^2 - 420^2) / (-2)(420)(950)

cos(A) = -0.186

Since A is an acute angle, we can take the inverse cosine to find its measure

A = cos⁻¹ (-0.186)

A ≈ 101.5°

The bearing of X from P is 35°, so the bearing of Y from X is

125° - 35° - A ≈ 54.5°

Therefore, the bearing of Y from X is approximately 54.5 degrees to the nearest minute.

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--The given question is incomplete, the complete question is given

" The bearings from a point P of two landmarks X and Y are 35° and 125° and their distances from P are 420 m and 950 m respectively. Find the bearing of Y from X (to the nearest minute)."--

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

When the number of milligrams reaches 11, the drug is to be injected again. We need approximately 6.7 hours between injections.

The given function is D(h)=30[tex]e^{-0.35h[/tex], which gives the number of milligrams D(h) of the drug in the patient's bloodstream h hours after it is injected.

When the drug is injected again, the number of milligrams in the bloodstream will be 11. Therefore, we need to find the value of h that satisfies the equation:

11 = 30[tex]e^{-0.35h[/tex]

To solve for h, we can first divide both sides by 30:

11/30 = [tex]e^{-0.35h[/tex]

Next, we take the natural logarithm of both sides:

ln(11/30) = ln([tex]e^{-0.35h[/tex])

Using the property of logarithms that ln(eˣ) = x, we can simplify the right side:

ln(11/30) = -0.35h

Finally, we can solve for h by dividing both sides by -0.35 and multiplying by -1:

h = (-1/0.35)ln(11/30)

Using a calculator, we get:

h ≈ 6.7

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Answer: x = 0

Step-by-step explanation:

simplify the expression

−5−3(6x−8)=−5x+19

−5−18+24=−5+19

19−18x=−5x+19

−18+19=−5+19

−5−3(6x−8)=−5x+19

−18x+19=−5x+19

−5−3(6x−8)=−5x+19

−18x+19=−5x+19

−18+19−19=−5+19−19

−18x=−5x+19 − 19

−18x+19−19=−5x+19 − 19

−18x=−5x

−18x+5x=−5x+5x

x=−5x+5x−13

x−13=−5+5

−13x=0

−13x/−13 = 0/-13

x= 0/−13

x= 0

The pitch of the roof is equal to 1.14

Since pitch of the roof is the angle between the roof and the horizontal line.

Pitch (slope) = V/H

Where, V represents the rising vertical distance of an object.

H represents the horizontal distance an object runs through.

Substituting the selected points into the formula, we have;

Pitch (slope) = 32/28

Pitch (slope) = 1.14

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a) the   proportion of even numbers in the population is 2/3 or approximately 0.667.

b. Sample Proportions and Probability Distribution Table is attched.

c) c. The mean of the sampling distribution of the sample proportion of even numbers is approximately 0.3333.

d. The sample poportion is a biased estimator of the population proportion because   the  sample proportions do not target the proportion of even numbers in   the population.

a. The population consists of 2, 6, and 7. The proportion of even numbers in the population is 1/3 since only 6 is even.

b. We can find the proportion of even numbers in each sample as follows:

2,2:   2/2 = 1

2,6: 1/2 = 0.5

2,7: 1/2  = 0.5

6,2: 1/2 =   0.5

6,6:   2/2 = 1

6,7: 1/ 2 = 0.5

7, 2: 1/2 = 0.5

7,6: 1/2 = 0.5

 7,7: 0/2   =0

This means that

   0 ⇒     1/9

  0.5⇒    5/9

   1  ⇒    3/9 (or 1/3)

So the above is summarized onto the table attached.

C)  The mean of the sampling distribution    of the sample proportion of even numbers is the weighted average of the possible values of the sample proportion,

where the weights are the probabilities of each value. Hence,

(0 x 1/9) +   (0.5 x 6/9 ) + (1 x 2/  9)

= 1/3

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Answer:

BFD

Step-by-step explanation:

Supplementary angles add to 180, or will form a straight line.

< AFB and angle BFD will form a straight line so they are supplementary.

a) The total amount that the Scotts ended up paying for the townhome (including the down payment and the monthly payments) is $445,144.80.

b) The total interest paid on the mortgage is $213,144.80.

The down payment is the advance payment made on a mortgage or loan to satisfy the lending concerning the borrower's financial capacity.

The down payment reduces the mortgage liability, including interest.

The cost of the townhome = $232,000

The down payment for the town home made by the Scotts = $48,000

The mortgage = $184,000 ($232,000 - $48,000)

Monthly payment = $1,103.18

The mortgage period = 360 months (30 years x 12)

The total payment on the mortgage over the mortgage period = $397,144.80 (1,103.18 x 360)

The total payment, including the down payment = $445,144.80 ($397,144.80 + $48,000)

The total interest paid = $213,144.80 ($445,144.80 - $232,000)

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The Scotts bought a townhome for $232,000. They made a down payment of $48,000 and took out a mortgage for the rest. Over the course of 30 years they made monthly payments of $1,103.18 on their mortgage until it was paid off.

The value of the expression 4/12 + 2/3 is 1 1/12

A fraction is a part of a whole. A fraction consist of the upper part( numerator ) and the lower part ( denominator). Examples of fractions are; simple fraction , complex fraction, mixed fraction, improper fraction.

In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Solving 4/12 + 1/3

= (9+4)/12

= 13/12

= 1 1/12

therefore the value of 4 twelfth + 2 third is 1 1/12

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Answer: The best estimate of the sum of the heights of the 5 mountains is between 130,000 and 135,000 ft. Therefore, option D is correct,

Step-by-step explanation: The best estimate of the sum of the heights of the five mountains listed is between 130,000 and 135,000 ft. These heights are already very high, so options A and B can be eliminated. Option C is too low, leaving option D as the best estimate.

Dhaulagiri: 26,810 ft

Nanga Parbat: 26,660 ft

Annapuma: 26,504 ft

Gasherbrum: 26,470 ft

Xixabangma: 26,286 ft

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If the helicopter flies 200 mph from the station nearest, the time it will it take to reach the ship is 0.52 hours

The numerical measurement between two entities or locations is defined as the distance, recorded in units such as kilometers, feet, meters, and miles. Determining the direct geometric line from point to point requires distinct models of calculation for both 2D and 3D geometry, most notably utilizing the Pythagorean theorem or the distance formula, respectively.

Physical sciences heavily rely on this notion, as it aids with computing rates that include: displacement, velocity, and acceleration. However, multiple factors - involving speed, direction, and time - can alter measured distances traveled by an object.

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

5 + 1/x = 11/5

Podemos simplificar esta ecuación multiplicando ambos lados por 5x, lo que da:

25x + 5 = 11x

Ahora, podemos resolver x aislando la variable en un lado de la ecuación:

25x - 11x = -5

14x = -5

x = -5/14

Por lo tanto, la solución a la ecuación es x = -5/14

The per cent of fruit juice in the mixture is 28%. The correct option is B.

To determine the percent of fruit juice in the mixture, we need to calculate the total amount of fruit juice in the 6 L of Brand A juice and the 9 L of Brand B juice, and then divide it by the total volume of the mixture.

The amount of fruit juice in 6 L of Brand A juice is:

0.52 x 6 L = 3.12 L

The amount of fruit juice in 9 L of Brand B juice is:

0.12 x 9 L = 1.08 L

The total amount of fruit juice in the mixture is:

3.12 L + 1.08 L = 4.20 L

The total volume of the mixture is:

6 L + 9 L = 15 L

So, the per cent of fruit juice in the mixture is:

(4.20 L / 15 L) x 100% = 28%

Therefore, the correct answer is (B) 28%.

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When an object turns 90 degrees around in a circle, it turns 1/4 of the way around in a circle. Therefore, the correct statement is: "It turns 1/4 of the way around in a circle."

To understand why an object turning 90 degrees around in a circle turns 1/4 of the way around in a circle, it's helpful to consider the relationship between angles and circles.

A circle is a geometric shape that is defined by a set of points that are equidistant from a center point.

The distance from the center point to any point on the circle is called the radius of the circle. The circumference of a circle is the distance around the circle, and it is equal to 2π times the radius.

A circle has a total angle of 360 degrees. When an object turns 90 degrees around in a circle, it covers only a quarter of the total angle.

Therefore, it turns 1/4 of the way around in a circle.

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Your question seems incomplete, the probable complete question is:

Which statement about an object turning 90 degrees around in a circle is true?

It turns 1/4 of the way around in a circle

It turns 2/4 of the way around in a circle

It turns 3/4 of the way around in a circle

It turns 4/4 of the way around in a circle

The value of number of years that the money was invested rounded to two decimal places is​, 2.5 years

We have to given that;

An amount of R1965,00 is invested in an account paying 11,50% interest per year, compounded semi-annually at the time of withdrawal the amount of interest earned is R633,75

Hence, We get;

Interest = P ( (1 + r/2)ⁿ - 1965)

R633.75 = 1965 (1 + 11.5%/2)ⁿ - 1965

1965 × 1.0575ⁿ - 1965 = 633.75

1965 × 1.0575ⁿ = 2598.75

1.0575ⁿ = 1.3225

n = log₁.₀₅₇₅ (1.3225)

n = 5

Hence, Number of years is, 5/2 = 2.5

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we can say that the pattern for how the numerator and denominator change in the fractions model is that they are multiplied or divided by the same non-zero integer.

Let's consider the fraction 2/ 3.

If we multiply both the numerator & the denominator by 2, we get 4 /6.

Also  multiplying both by 3, we will  get 6 /9

In general,  if we multiply the numerator and the denominator by the same non-zero integer, we get an equivalent fraction.

On the other hand, if we divide both the numerator and   the denominator by the same non-zero integer,

we also get an equivalent fraction. For example    if we divide 6/9 by 3, we get 2/3 again.

Hence , the above conclusion is correct.

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Full Question:

Fraction 2/ 3.

What pattern can you use to describe how the numerator and denominator change in the fraction models above?

It is very likely that a vacuum will last between 5.5 and 7.5 years.

This is because we can use the properties of the normal distribution to calculate that about 68% of the vacuum cleaners will fall within one standard deviation of the mean, which in this case is between 6.5 - 0.5 = 6 and

6.5 + 0.5 = 7

About 95% of the vacuum cleaners will fall within two standard deviations of the mean, which in this case is between 6 - 0.5 = 5.5 and 6.5 + 0.5 = 7

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The perimeter of the composite figure that is given above would be = 96.6m.

To calculate the perimeter of the given shape, it has to be divided into two.

First shape is a rectangle. Therefore the perimeter of a rectangle is calculated with the formula = 2(l+w)

Where ;

length = 16m

width = 11m

perimeter = 2(16+11)

= 2×27

= 54m

The second shape:

Perimeter of triangle = l+w+h

where;

length = 18-11 = 7m

width = 16m

height = 19.5m

perimeter = 7+16+19.5 = 42.5m

Therefore, the perimeter of the shape = 54+42.5 = 96.6m

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The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

We have to given that;

Zeroes of the polynomial are,

⇒ 7, i

Now, The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = (x - 7)² (x - i)

⇒ P (x) = (x² + 49 - 14x) (x - i)

⇒ P (x) = (x³ - ix² + 49x - 49i - 14x² + 14ix)

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

Thus, The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

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The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Option B is the correct answer.

We have,

The following data set shows the values collected by the manager.

{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3}

Now,

We make the stem and leaf plot as:

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

Here,

3 can be written as 03 and 0 can be written as 00.

Thus,

The stem and leaf plot that correctly represents the data sets is

Stem    Leaf

0      |  0, 3        

1       |  7, 7, 7, 1, 7,

2      |  8, 8, 2, 4, 0. 0

3      |   3, 1,

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7. Radius of circle P = 2       Radius of circle Q = 1

Coordinates of the point of tangency (4,2)

The equation of the tangency line is x = 4

8. AB is not a tangent. BC² ≠ AB² + AC²

9. The three radii of the circle are; CB, CF and CD

A diameter of the circle is BD

A tangent of the circle is GE

A chord of the circle is BD

A secant of the circle is AD

A point of tangency is F

7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.

The radius then is 4/2 = 2.

The radius of circle q is 2/2 = 1

You could also use the formula

Distance = sqrt((x2 - x1)² + (y2 - y1)²)

8. √4² + √12² = √160

√13 = 169

Therefore AB is not tangent. It is less than BC

9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's

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The given Mayan number which is : :|| :|| in decimal (base 10) is 42.

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

To convert the given Mayan number to decimal (base 10), we need to understand the positional value of each symbol. Each position in the number represents a power of 20, with the rightmost position being 20⁰, the next position to the left being 20¹, and so on.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represents a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represents a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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Complete question is:

Convert the following Mayan number to decimal (base 10).

: :|| :||

Answer:

C

Step-by-step explanation:

given

cosΘ = [tex]\frac{9}{15}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]

then to find the third side (opposite) use Pythagoras' identity

opposite² + 9² = 15²

opposite² + 81 = 225 ( subtract 81 from both sides )

opposite² = 144 ( take square root of both sides )

opposite = [tex]\sqrt{144}[/tex] = 12

then

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{9}[/tex]

The number of residents Town A used to have is 1400, and the number of residents Town B used to have is 3600, as shown by the simple equation below.

Let x be the number of residents Town A used to have. The number of residents in Town B is:

5000 - x

We know that Town A had 12% whites and Town B had 10% whites. After the merge, the percentage of whites is 10.56%. With that in mind:

12%x+10%(5000-x) = 10.56%(5000)

0,12x + 500 - 0,1x = 528

0.02x = 28

x = 1400

Therefore, the number of residents Town A used to have is 1400. Now, the number of residents town B used to have is:

5000 - 1400 = 3600

With that in mind, we can conclude our answer is correct.

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The Area of Triangle is 10 square unit.

We have,

base = 4 unit

Height = 5 unit

So, Area of Triangle

= 1/2 x base x height

= 1/2 x 4 x 5

= 2 x 5

= 10 square unit

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The test statistic is z₀ = 2.65 and the P-value is 0.004. The null hypothesis is rejected at the 5% level of significance, and we conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8.

To test the hypothesis using the P-value approach, we can follow these steps:

Check whether the sample size is large enough for the normal approximation to the binomial distribution. The requirements are satisfied if np₀ >= 10 and n(1-p₀) >= 10,

where p₀ is the hypothesized proportion under the null hypothesis. In this case, p₀ = 0.8, n = 125, so np₀ = 100 and n(1-p₀) = 25, both of which are greater than 10.

Set up the null and alternative hypotheses.

The null hypothesis is H₀: p = 0.8 (the true proportion is 0.8).

The alternative hypothesis is H₁: p > 0.8 (the true proportion is greater than 0.8).

Calculate the test statistic.

Under the null hypothesis, the test statistic follows a standard normal distribution.

The test statistic is calculated as:

z₀ = (x - np₀) / sqrt(np₀(1-p₀))

where x is the number of successes in the sample.

Plugging in the values, we get:

z₀ = (105 - 1250.8) / √(1250.8 x 0.2)

z₀ = 2.65

Calculate the P-value.

The P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true.

Since this is a right-tailed test (H₁: p > 0.8), we calculate the area to the right of the test statistic.

Using a standard normal table or calculator, we find that the area to the right of z₀= 2.65 is 0.004.

Therefore, the P-value is 0.004.

Make a decision and interpret the results.

Using a significance level of α = 0.05, we compare the P-value to α.

Since the P-value (0.004) is less than α (0.05), we reject the null hypothesis.

We conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8 at a 5% level of significance.

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The solution for integrals are -1/3 (2 + cos² (x))[tex]^\frac{3}{2}[/tex]  +C

If we are finding the following integral below

∫ (√2 + (cos x)² / secx × cscx) dx instead of ∫ (√(2 + cos²x)) / (secx × csc) dx

then

secx = 1/cosx and cscx = 1/sinx

∫ (√(2 + cos²x)) × sinx × cosx dx

givn that sin²x + cos²x = 1

sin²x = 1 - cos²x

u = cosx,

du = -sinx dx.

-∫ (√u) / (2sinxcosx) du.

-√u + C.

When you substitute the original equation into the result

1/3 (2 + cos²x)^(3/2) + C.

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The area of the rectangle is 81 square units. (option a)

To find the area of a rectangle, we need to know its length and width. We can determine these values by looking at the difference between the x-coordinates and the y-coordinates of the vertices.

In this case, we have the following coordinates: (-4,5), (5,5), (-4,-4), and (5,-4).

The length of the rectangle is the difference between the x-coordinates of the left and right vertices:

=> 5 - (-4) = 9.

The width is the difference between the y-coordinates of the top and bottom vertices:

=> 5 - (-4) = 9.

To find the area of the rectangle, we multiply its length by its width:

=> 9 x 9 = 81.

So, the correct answer is the (a), 81 square units.

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