batman is taking a midnight stroll through gotham and sees the bat signal in the sky . if batman is 320 feet from the foot of the bat signal and the angle of elevation is 42* , find the height of the bat signal?

Yes, the quadrilateral is a parallelogram. To prove this using the distance formula method, we need to show that opposite sides of the quadrilateral are equal in length.

We can calculate the distance between each pair of points using the distance formula:

d = [tex]\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Using this formula, we get:

d(LM) = √[tex]((5 - (-1))^2 + (8 - 6)^2)[/tex] = √(36 + 4) = √(40) = 2√(10)

d(NP) = √[tex]((-8 - 0)^2 + (12 - 2)^2)[/tex] = √(64 + 100) = √(164) = 2√(41)

d(LN) = √[tex]((0 - (-1))^2 + (2 - 6)^2)[/tex] = √(1 + 16) = √(17)

d(MP) = √[tex]((-8 - 5)^2 + (12 - 8)^2[/tex]) = √(169 + 16) = √(185)

We can see that d(LM) = d(NP) and d(LN) = d(MP), which means that opposite sides of the quadrilateral are equal in length. Therefore, the quadrilateral is a parallelogram.

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Step-by-step explanation:

2x + 2y  = 28   <=====given

x * y = 40     <===given .....  re-arrange to :

           y = 40 / x    <===substitute this 'y'  into the first equation

2x + 2 ( 40/x) = 28   <=====solve for x

2x^2 -28x + 80 = 0

x^2 -14x +40 = 0

(x -10)(x-4) = 0                        shows x = 10 or 4    then y = 4 or 10

dimensions    10    and 4   inches

Answer:

4 or 10 inches

Step-by-step explanation:

I added a photo of my solution

The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was 261. Use this price as the population mean and assume the population standard deviation of preparation fees is 120.

We need to find the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

We use the central limit theorem that states that, regardless of the shape of the population, the sampling distribution of the sample means approaches a normal distribution with mean μ and standard deviation

σ/√n

where μ is the population mean, σ is the population standard deviation, and n is the sample size.

Therefore, we have:

[tex]\mu = 261\]\\sigma = $120\]\\n = 20\][/tex]

[tex]S.E.= \frac{\sigma}{\sqrt{n}}\\S.E =\frac{\ 120}{\sqrt{20}}\\S.E =26.83[/tex]

The probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is given by:

[tex]P(Z < \frac{X - \mu}{S.E})\][/tex]

where X is the sample mean, μ is the population mean, and S.E is the standard error of the mean.

To calculate the probability, we standardize the distribution of the sample means using the z-score formula, i.e.,

[tex]\[z = \frac{X - \mu}{S.E} = \frac{\50 - \261}{\26.83} = -7.91\][/tex]

Therefore, the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is zero because the z-score is less than the minimum z-score (i.e., -3.89) that corresponds to the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

Thus, it is impossible to obtain such a sample.

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A horizontal curve is to be designed with a 2000 feet radius. The curve has a tangent length of 400 feet and its pi is located at station 103+00. Determine the stationing of the PT.

A horizontal curve is a curve that is used to provide a transition between two tangent sections of a roadway. To connect two tangent road sections, horizontal curves are used. Horizontal curves are defined by a radius and a degree of curvature. The curve's radius is given as 2000 feet. The tangent length is 400 feet.

The pi is located at station 103+00.

To determine the stationing of the PT, we must first understand what the "pi" means. PC or point of curvature, PT or point of tangency, and PI or point of intersection are the three primary geometric features of a horizontal curve. The point of intersection (PI) is the point at which the back tangent and forward tangent of the curve meet. It is an important point since it signifies the location of the true beginning and end of the curve. To calculate the PT station, we must first determine the length of the curve's arc. The formula for determining the length of the arc is as follows:

L = 2πR (D/360)Where:

L = length of the arc in feet.

R = the radius of the curve in feet.

D = the degree of curvature in degrees.

PI (103+00) indicates that the beginning of the curve is located 103 chains (a chain is equal to 100 feet) away from the road's reference point. This indicates that the beginning of the curve is located 10300 feet from the road's reference point. Now we need to calculate the degree of curvature

:Degree of curvature = 5729.58 / R= 5729.58 / 2000= 2.8648 degrees. Therefore, the arc length is:

L = 2πR (D/360)= 2π2000 (2.8648/360)= 301.6 feet.

The length of the curve's chord is equal to the length of the tangent, which is 400 feet. As a result, the length of the curve's long chord is: Long chord length = 2R sin (D/2)= 2 * 2000 * sin(2.8648/2)= 152.2 feet To determine the stationing of the PT, we can use the following formula: PT stationing = PI stationing + Length of curve's long chord= 10300 + 152.2= 10452.2Therefore, the stationing of the PT is 10452+2.

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qwerty

2.8% the answer is 2.8% and b is 2.8%

The compound inequality is -7 < y/3 - 2 < 4 and the solution is -15 < y < 18

To write the compound inequality that represents the statement, we can first translate the words into symbols:

The quotient of a number y and 3, less 2: y/3 - 2

Is between -7 and 4: -7 < y/3 - 2 < 4

So the compound inequality that represents the statement is:

-7 < y/3 - 2 < 4

To solve this compound inequality, we can first add 2 to all parts of the inequality:

-7 + 2 < y/3 - 2 + 2 < 4 + 2

Simplifying, we get:

-5 < y/3 < 6

To isolate y/3, we can multiply all parts of the inequality by 3:

-15 < y < 18

Therefore, the solution to the compound inequality is: -15 < y < 18

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You have a 4/12 probability.

Answer:

Step-by-step explanation:

Circle centre: (4,7)

Radius: 3

Equation is:

  [tex](x-h)^2+(y-k)^2=r^2[/tex]   (where (h,k) is center, r is radius)

  [tex](x-4)^2+(y-7)^2=3^2[/tex]

  [tex](x-4)^2+(y-7)^2=9[/tex]     (This is the general standard form )

in expanded form,

  [tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]

  [tex]x^2+y^2-8x-14y+56=0[/tex]

Note: Unless stated either form is an acceptable answer.

Answer: 15.5

Step-by-step explanation:

H = A/B

= 186/12

= 15.5

By probability , 3 Apples are left .

What does a probability simple definition entail?

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

                             The probability is a metric for determining how likely an event is to occur. It gauges how likely an event is. The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.

Jhoney ate =  3 apples

           = 2 left

  he eat = ³C₂

              =  3!/(3-2)! 2!

              = 3

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The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is [tex]1/144[/tex]

The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.

Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:

P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)

[tex]= (1/6) \times (1/6) \times (1/2) \times (1/2)[/tex]

[tex]= 1/144[/tex]

Therefore, the probability that Kyle wins the prize is ,[tex]1/144[/tex] or approximately  [tex]0.0069[/tex] (rounded to four decimal places).

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The total amount paid by Jennifer for 14.75 gallons of gasoline at the cost of $2.95per gallons is equal to $43.51.

Total gallons of gasoline bought by Jennifer for her car = 14.75 gallons

Cost of gasoline per gallons = $2.95

The total amount Jennifer paid for the gasoline is equal to,

Amount paid by Jennifer

= Number of gallons of gasoline x Cost per gallon

Substitute the value in the formula we get,

⇒ Amount paid by Jennifer = 14.75 gallons x $2.95/gallon

⇒ Amount paid by Jennifer = $43.5125

⇒ Amount paid by Jennifer = $43.51

Therefore, the closest amount Jennifer paid for the gallons of gasoline is equal to $43.51.

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Answer:

x=8

Step-by-step explanation:

8 x 8 = 64

You can find this answer by using inverse operations.

64/8 = 8

To check your work, you can multiply...

8x8 = 64.

Hope this helps!

6.81 is the Ph of a neutral aqueous solution.

To calculate the pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴, follow these steps:

1. Identify that in a neutral aqueous solution, the concentrations of hydrogen ions (H⁺) and hydroxide ions (OH⁻) are equal. Therefore, [H⁺] = [OH⁻].

2. Use the KW expression, which is the product of [H⁺] and [OH⁻] concentrations. In this case, KW = 2.4×10⁻¹⁴.

3. Since [H⁺] = [OH⁻], you can rewrite the KW expression as KW = [H⁺]². Now, solve for [H⁺] by taking the square root of KW: [H⁺] = sqrt(KW) = sqrt(2.4×10⁻¹⁴).

4. Calculate the square root: [H⁺] ≈ 1.55×10⁻⁷ M.

5. Use the pH formula: pH = -log[H⁺]. Plug in the [H⁺] value: pH = -log(1.55×10⁻⁷).

6. Calculate the pH: pH ≈ 6.81.

The pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴ is approximately 6.81.

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A) Jane's share is 12% of X, which is equal to 0.12X.

B) the total cost of the insurance is $20,691.67

C)  the employer's share is $18,208.67.

Total cost is the collective term for the cost of production as a whole, which encompasses both fixed and variable costs. The expense necessary to produce a good is referred to in economics as the total cost. There are two parts that make up the total cost: a set price The expense is what never changes.

Let X be the total cost of Jane's individual health care, then:

A) Jane's share is 12% of X, which is equal to 0.12X.

B) We know that Jane's deduction from each biweekly paycheck is $95.50, so she pays a total of:

$95.50 * 26 = $2,483

This amount is equal to 0.12X, so we can set up an equation:

0.12X = $2,483

Solving for X, we get:

X = $20,691.67

Therefore, the total value of the insurance is $20,691.67.

C) The employer's share is the difference between the total cost of the insurance and Jane's share:

Employer's share = Total cost - Jane's share

Employer's share = $20,691.67 - $2,483

Employer's share = $18,208.67

Therefore, the employer's share is $18,208.67.

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Jane's share of the total cost of her individual health care is $795.83, The total value of the insurance is $795.83 + 0.88x and the employer's share is 0.88x.

What is cost?

In mathematics, cost refers to the amount of resources (such as money, time, effort, or materials) that are required to produce or obtain something.

A) To find Jane's share of the total cost of her individual health care, we can use the information that she contributes 12% of the cost, and that this is a $95.50 deduction from each of her biweekly paychecks.

Let x be the total cost of Jane's individual health care. Then:

12% of x = $95.50

0.12x = $95.50

x = $95.50 / 0.12

x = $795.83

Therefore, Jane's share of the total cost of her individual health care is $795.83.

B) To find the total value of the insurance, we can add up both Jane's share and the employer's share.

If Jane is contributing 12% of the total cost, then the employer is contributing the remaining 88% of the cost. So the employer's share can be calculated as:

88% of x = 0.88x

The total value of the insurance is then:

Total value = Jane's share + Employer's share

Total value = $795.83 + 0.88x

C) To calculate the employer's share, we can use the same information as above. The employer is contributing 88% of the total cost, so:

88% of x = 0.88x

Therefore, the employer's share of the total cost of Jane's individual health care is $0.88x, or approximately $700.33 (if we use the value of x that we found in part A).

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As the given abc is a right triangle with points a(2, 5), b(2, 0), and c(x, 0). The area of 'abc' is 25 square units. and the equation of AC is x = 5√5.

The equation of ac has to be found. Since triangle ABC is right-angled, it can be shown that

                  AC² = AB² + BC²

    Finding the lengths of AB and BC before using the Pythagorean theorem to find AC.

    Using the distance formula,

                     AB =√(5²+0²)

                           = √25

                          = 5,

           And BC = √(x²+0²)

                         = √x²

                          = x.

  Area of a right triangle = ½(base × height)

          Here base = AB and height = BC,

              So,  ½ × 5 × x = 25

                            ⇒ 5x = 50

                              ⇒ x = 10

       Now, to find AC, use the Pythagorean Theorem.

                      AC² = AB² + BC²

                             = 5² + 10²

                             = 25 + 100

                             = 125AC

                             = √125

                             = 5√5

     Thus, the equation of AC is x = 5√5. Answer: x = 5√5.

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There is a probability of around 60% that during a week picked randomly, the combined sum of their earnings will be below $0.2533.

The given probability is a measure of the chances that the occurrence of an event will happen. In the context of the question, we want to calculate the combined total of earnings that are less than a certain amount. We know that the probability is approximately 0.6. Therefore, the answer is given by the value that satisfies this condition.

That is, P(X < a) = 0.6where X represents the combined total earnings of a randomly selected week, and a is the required amount.

To solve for a, we can use the cumulative distribution function (CDF) of X. The CDF gives the probability that X is less than or equal to a. Therefore, CDF(a) = P(X ≤ a)

The complement of this probability isP(X > a) = 1 - CDF(a)

We know that P(X < a) = 0.6, which is equivalent to (X ≤ a) = P(X < a) + P(X = a) = 0.6 + 0 = 0.6

Therefore, P(X > a) = 1 - CDF(a) = 1 - P(X ≤ a) = 1 - 0.6 = 0.4

Now we can use a calculator to find the value of a that corresponds to P(X > a) = 0.4.

For example, if we use a calculator, we get a value of a = 0.2533 (rounded to four decimal places).

Therefore, the probability is approximately 0.6 that in a randomly selected week, they will make a combined total of less than $0.2533.


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The inequality that represents Miguel's spending limit is $16.00 ≤ x.

Let x represent the total amount of money Miguel wants to spend. We know he spent $10.49 on popcorn and can spend up to $5.51 on a drink.

To find the inequality, we can add these two amounts together and set it less than or equal to x, since x represents the maximum amount he wants to spend. Mathematically, we can write:

$10.49 + $5.51 ≤ x

Simplifying this inequality, we get:

$16.00 ≤ x

This means that Miguel can spend up to $16.00 in total on the popcorn and drink combined. If he spends more than $16.00, he will have exceeded his limit.

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Two events that are collectively exhaustive are event 1: a value of 6 or more and event 2: a value of 7 or less.

These events are collectively exhaustive because the events cover the entire possible range of values of the dice rolls. If one of these events does not occur, then the other event must occur. This means that the sum of the dice rolls is either 6 or less, or it is greater than 6. This means that the sum of the dice rolls is either 7 or more, or it is less than 7.

Another set of events that are collectively exhaustive are event 1: rolling an even number and event 2: rolling an odd number. These events are collectively exhaustive because the events cover the entire set of possible outcomes of rolling two dice. If one of these events does not occur, then the other event must occur. This means that the sum of the dice rolls is either even or odd. This means that the sum of the dice rolls is not both even and odd at the same time.

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The graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.

To make an opening or hollow structure wider or larger than usual, such as a blood vessel or the pupil of an eye.

The process of dilation entails growing an object's size without changing its shape.

The size of the object may rise or decrease depending on the scale factor.

Using dilation maths, a square with a side of 5 units can be made wider to have a side of 15 units, yet the square retains its original shape.

So, the coordinates of each vertex of the figure are multiplied by the scale factors to create a dilatation in the image.

The vertices for the original figure that was graphed are listed as follows:

I(0,6).

H(3,6).

G(9,0).

F(-6,-9).

E(-6,-6).

The coordinates of the resulting image are presented as follows since the dilation has a scale factor of 1/3, which means that the coordinates are multiplied by 1/3:

I'(0,2).

H'(1,2).

G'(3,0).

F'(-2,-3).

E'(-2,-2).

Therefore, the graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.

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Correct question:

The figure below is dilated by a factor of centered at the origin. Plot the resulting image. -109 -11 E Click twice to plot a segment. Click a segment to delete it. 4 -5 7 F A -9 10 9 B 4 I d 3 P BI 1 9 H 3 4 6 6 M​

Answer:

= 58/33

= 1 25/33

Step-by-step explanation:

12/11 - (-2/3) =

= 12/11 + 2/3

= 36/33 + 22/22

= 58/33

= 1 25/33

The percent decrease in the price of the headphones is 26.32%.

Explanation:

To find the percent change in price, we can use the following formula:

percent change = (new value - old value) / old value * 100%

     
In this case, the old value is the original price of the headphones, which is $95.
   

The new value is the sale price, which is $70. Plugging these values into the formula, we get:percent change = (70 - 95) / 95 * 100%

percent change = -25 / 95 * 100%

percent change = -0.2632 * 100%

percent change = -26.32%

   
The negative sign indicates that the price has decreased, and the magnitude of the percent change is 26.32%, which means that the sale price is 26.32% lower than the original price.

The scale factor used to create the dilated polygon is 4.

What is scaler factor?

Scale factor is a numerical ratio that describes how much a geometric figure has been enlarged or reduced. It is the ratio of the length of a side, diagonal, or any other linear dimension of the new (dilated) figure to the corresponding dimension of the original figure.

The distance between two points can be calculated using the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.[/tex]

To determine the scale factor, we need to compare the distances between corresponding points in the original and dilated polygons. Let's start by finding the distance between points A and B in the original polygon:

[tex]$d_{AB}=\sqrt{(3-1)^2+(-1+1)^2}=\sqrt{4}=2$[/tex]

Now let's find the distance between corresponding points A' and B' in the dilated polygon:

[tex]$d_{A'B'}=\sqrt{(12-4)^2+(-4+4)^2}=\sqrt{64}=8$[/tex]

To find the scale factor, we divide the corresponding distances:

[tex]$scale\ factor=\frac{d_{A'B'}}{d_{AB}}=\frac{8}{2}=4$[/tex]

Therefore, the scale factor used to create the dilated polygon is 4.

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Therefore, the total number of sets of four marbles, including exactly two green marbles, is 720.

The given bag contains a total of [tex](2+4+1+6+5)=18[/tex] marbles.

There are two possibilities of selecting two green marbles and the other two marbles in a set, as shown below;GG -- NN (No Green Marbles)GG -- RR (No Green Marbles)GG -- YY (No Green Marbles)GG -- OO (No Green Marbles)GG -- GL (Lavender)GG -- RG (Red)GG -- OG (Orange)

The first two options have no green marbles; thus, they are eliminated. We can select non-green marbles in C(16,2) = 120 ways, then multiply by C(4,2) = 6 to choose two green marbles out of four.So, the total number of such sets is

[tex]120 × 6 = <<120*6=720>>720.[/tex]

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The evaluation of the algebraic expression 8a-1+0.5b when a=1/4 and b=10 is 6.

We are given an expression 8a−1+0.5b8, and we are asked to evaluate it when a = 1/4 and b = 10. Substituting these values, we get:

8(1/4) - 1 + 0.5(10) = 2 - 1 + 5

Simplifying the expression on the right-hand side, we get:

8a−1+0.5b8 = 6

Therefore, when a = 1/4 and b = 10, the value of the expression 8a−1+0.5b8 is 6.

This means that if we substitute the given values for a and b, the resulting expression will have a value of 6. It is important to correctly substitute the values before evaluating the expression to obtain the correct answer.

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____The given question is incomplete, the complete question is given below:

Evaluate 8 a − 1 + 0.5 b 8a−1+0.5b8, a, minus, 1, plus, 0, point, 5, b when a = 1 4 a= 4 1 a, equals, start fraction, 1, divided by, 4, end fraction and b = 10 b=10b, equals, 10.

Answer:

The first step is to calculate the interest that accrues over the 3-month period:

Interest = Principal x Rate x Time

= $4,000 x 0.075 x (3/12)

= $75

The amount due on the loan is the sum of the principal and interest:

Amount due = Principal + Interest

= $4,000 + $75

= $4,075

Rounding to the nearest cent gives: $4,075.00

Answer:

x= 2

Step-by-step explanation:

² means times the number itself 2 times.

2×2=4

Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff. Dan had 320 stickers first.

Dan had 50% fewer stickers than Jeff.

After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers).

How many stickers did Dan have at first?

The total number of stickers that Jeff had is denoted by J, and the total number of stickers that Dan had is denoted by D.

In order to solve the question, let us first represent the given data mathematically:

J = 1.5D; D+20 = 0.6(J-20)

We have 2 equations and 2 unknowns, J and D.

We can solve these equations using simultaneous linear equations.

Substitute the first equation in the second equation:

D+20=0.6(J-20)

⇒ D+20=0.6J-12

⇒ D=0.6J-32

Now substitute the value of D in the first equation:

J=1.5D

⇒ J=1.5(0.6J-32)

⇒ J=0.9J-48.

Therefore, J=480

The total number of stickers that Jeff had initially was 480.

Now, to calculate the total number of stickers that Dan had, we can use the equation

J=1.5D:J=1.5D

⇒ 480=1.5D

⇒ D=320

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When the tank is tilted, the water level reaches the midpoint of the 60 cm side, which is 30 cm from the bottom of the tank. This means that the height of the water is 30 cm.

To find the depth of the water when the tank is returned to its horizontal position, we need to use the concept of similar triangles. The two triangles formed by the water level and the sides of the tank are similar, because they have the same angles.

Let x be the depth of the water in centimeters when the tank is returned to its horizontal position. Then we have:

(40 - x) / 60 = 30 / 50

Simplifying this equation, we get:

40 - x = 36

x = 4

Therefore, the depth of the water in the fish tank when it is returned to its horizontal position is 4 cm.