A triangle drawn on a map has sides that measure 7 cm, 14 cm, and 12 cm. the shortest of the corresponding real-life distances is 120 km. find the longest of the real-life distances.

The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.

In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.

The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.

The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.

While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.

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Answer:

1.414214

Step-by-step explanation:

I think this is right lol.

Answer:

x=-1 y=2

Step-by-step explanation:

Use Elimination or Substitution (Elimination shown below)

6x+5y=4

6x-7y =-20 <- Multiply by -1

-6x+7y=20

12y = 24

y=2

Plug back into either of the equations and solve for x.

6x + 10= 4

6x = -6

x = -1

Double check work:

-6+10 = 4

The solution of each part of the question is given below:

a. Let C be the event that a person smokes cigars, and let S be the event that a person smokes cigarettes. The percentage of Americans who smoke either cigars, cigarettes, or both can be calculated as P(C U S), where U represents the union of two events. From the given information, P(C) = 15% and P(S) = 35%. The probability that a person smokes both cigars and cigarettes is 7%, so P(C ∩ S) = 7%.

P(C U S) = P(C) + P(S) - P(C ∩ S)

P(C U S) = 15% + 35% - 7% = 43%

So, 43% of Americans smoke either cigars, cigarettes, or both.

b. The percentage of Americans who smoke neither cigars nor cigarettes can be calculated as P(C' ∩ S'), where C' represents the complement of event C (not smoking cigars) and S' represents the complement of event S (not smoking cigarettes).

P(C' ∩ S') = 100% - P(C U S)

P(C' ∩ S') = 100% - 43% = 57%

So, 57% of Americans smoke neither cigars nor cigarettes.

c. The percentage of Americans who smoke cigars but not cigarettes can be calculated as P(C ∩ S').

P(C ∩ S') = P(C) - P(C ∩ S)

P(C ∩ S') = 15% - 7% = 8%

So, 8% of Americans smoke cigars but not cigarettes.

d. The conditional probability that a person smokes cigarettes given that he smokes cigars can be calculated as P(S | C), where S represents the event that a person smokes cigarettes and C represents the event that a person smokes cigars.

P(S | C) = P(S ∩ C) / P(C)

P(S | C) = 7% / 15% = 0.47

So, the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars is 0.47, or 47%.

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Answer:

Step-by-step explanation:

4x + 2y - 16z - (-12x + 2y - 4z)

4x + 2y - 16z + 12x - 2y + 4z

16x - 12z

The limit of a convergent sequence of complex numbers is unique.

To show that the limit of a convergent sequence of complex numbers is unique by appealing to the corresponding result for a sequence of real numbers,

we use the fact that a sequence of complex numbers can be represented as a sequence of ordered pairs of real numbers.

Let {z_n} be a sequence of complex numbers with two distinct limits, say a and b.

Then we can writez_n = (x_n, y_n) where x_n and y_n are the real and imaginary parts of z_n, respectively.

Since {z_n} converges to a,

we have both x_n -> Re(a) and y_n -> Im(a) as n -> infinity.

Similarly, since {z_n} converges to b,

we have both x_n -> Re(b) and y_n -> Im(b) as n -> infinity.

Using the corresponding result for a sequence of real numbers,

we can conclude that {x_n} converges to Re(a) and to Re(b), while {y_n} converges to Im(a) and to Im(b).

However, the limit of a product of two sequences is the product of their limits if both limits exist.

Therefore, we havez_n = (x_n, y_n) -> (Re(a), Im(a)) andz_n = (x_n, y_n) -> (Re(b), Im(b))as n -> infinity, which implies that (Re(a), Im(a)) = (Re(b), Im(b)).

Hence, a = b, and the limit of a convergent sequence of complex numbers is unique.

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The general solution is \($$y=c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x \text {. }$$\)

Consider the following differential equation: y'' − y = cosh x

The given differential equation in the operator form will be: (D^2-1)y=coshx

The auxiliary equation of the corresponding homogeneous equation will be:

m^2-1 = 0

=>m^2=1

=>m=+1,-1

So, the complementary function will be \(y_c=c_1 e^x+c_2 e^{-x}.\alpha\)

Now, let \(y_1=e^x, y_2=e^{-x}.\)

Compute the Wronskian determinant:

\($$\begin{aligned}W\left(y_1, y_2\right) & =\left|\begin{array}{ll}y_1 & y_2 \\y_1^{\prime} & y_2^{\prime}\end{array}\right| \\& =\left|\begin{array}{ll}e^x & e^{-x} \\e^x & -e^{-x}\end{array}\right| \\& =-e^x e^{-x}-e^x e^{-x} \\& =-2\end{aligned}$$\)

Since the given differential equation is already in the form \($y^{\prime \prime}+P(x) y^{\prime}+Q(x) y=f(x)$\) (that is, the coefficient of y'' is 1 ),

So identify:

f(x)=cosh x

Then, calculate the values of u_1' and u_2', using formulas as follows:

\($$\begin{aligned}u_1^{\prime} & =-\frac{y_2 f(x)}{W} & u_2^{\prime} & =\frac{y_1 f(x)}{W} \\& =-\frac{e^{-x} \cdot \cosh x}{-2} & & =\frac{e^x \cdot \cosh x}{-2} \\& =\frac{e^{-x} \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} & \text { and } & =-\frac{e^x \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} \\& =\frac{1}{4}\left(1+e^{-2 x}\right) & & =-\frac{1}{4}\left(e^{2 x}+1\right)\end{aligned}$$\)

Integrate on both sides of u_1' and u_2' with respect to ' x', to get:

\($$u_1=\frac{x}{4}-\frac{e^{-2 x}}{8} \text { and } u_2=-\frac{x}{4}-\frac{e^{2 x}}{8} .$$\)

So, the particular solution is,

\($$\begin{aligned}y_p & =u_1 y_1+u_2 y_2 \\& =\left(\frac{x}{4}-\frac{e^{-2 x}}{8}\right) e^x+\left(-\frac{x}{4}-\frac{e^{2 x}}{8}\right) e^{-x} \\& =\frac{1}{4} x\left(e^x-e^{-x}\right)-\frac{1}{8}\left(e^{-x}+e^x\right) \\& =\frac{1}{2} x \sinh x-\frac{1}{8}\left(e^{-x}+e^x\right)\end{aligned}$$\)

Thus, the general solution of the given differential equation is,

\($$\begin{aligned}y & =y_c+y_p \\& =c_1 e^x+c_2 e^{-x}+\frac{1}{2} x \sinh x-\frac{1}{8} e^{-x}-\frac{1}{8} e^x \\& =\left(c_1-\frac{1}{8}\right) e^x+\left(c_2-\frac{1}{8}\right) e^{-x}+\frac{1}{2} x \sinh x \\& =c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x\end{aligned}$$\)

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Answer:

12x-4=80

12x=80+4

=84

x=84÷12

=7

Answer:

The answer is B. i.e. 6.6units.

Answer:

Area=88in squared

Step-by-step explanation:

Answer 128 to the second  power

explanation:

its 128 to the second power because if you multiply 16*8 and you will get 128to the second power

Answer: A) AC=DF

Step-by-step explanation:

Angle-Side-Angle (ASA) Postulate: If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

Answer A is the only one that wouldn’t help you prove that these triangles are congruent.

The measure of angle EDF from the given figure is 23°.

From the given figure, ∠EGF=23°.

The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

By using angles in the same segment theorem, we get

∠EGF = ∠EDF = 23°

Therefore, the measure of angle EDF from the given figure is 23°.

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Answer:

  d/3

Step-by-step explanation:

For k = 8c, the concentration is ...

  S = c/x^2 + 8c/(d -x)^2

The minimum of the function will be found where its derivative is zero. The derivative with respect to x is ...

  S' = -2c/x^3 +(-2)(8c)(-x)/(d -x)^3

We are interested in the value of x that makes this zero.

  0 = -2c/x^3 +16c/(d -x)^3 . . . . . simplify slightly, set S'=0

  0 = (-2(d -x)^3 +16x^3)/(x(d -x))^3 . . . . . combine terms, divide by c

  0 = d^3 -3d^2x +3dx^2 -x^3 -8x^3 . . . . multiply by (x(d-x))^3/(-2)

  9x^3 -3dx^2 +3d^2x -d^3 = 0 . . . . . simplified cubic

Factoring by grouping, we have ...

  (9x^3 -3dx^2) +(3d^2x -d^3) = 0

  3x^2(3x -d) +d^2(3x -d) = 0

  (3x^2 +d^2)(3x -d) = 0

The solution will be found where the second of these factors is zero:

  3x -d = 0

  x = d/3

The concentration of the deposit is a minimum at x = d/3 miles.

_____

The graph shows the minimum is x = 1/3 when d = 1.

Answer:

P(1,2)  m = 3    Since you are given a point and a slope, use the point-slope form for the equation of a line: y - y1 = m(x - x1)

y - 2 = 3(x - 1)

y - 2 = 3x - 3

y = 3x - 1 hope this helps

Step-by-step explanation:

Answer

y=3x+1

put in point slope form y-yone=m(x-x one)

y+2=3(x+1)

y+2=3x+3

y=3x+1

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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To determine Km from a double-reciprocal plot, you would choose option (A) which is to multiply the reciprocal of the x-axis intercept by -1.

In the double-reciprocal plot equation, the x-axis intercept is -1/Km, and the y-axis intercept is 1/Vmax. Therefore, if you take the reciprocal of the x-axis intercept, you get -Km, and multiplying it by -1 gives you Km.

This method is preferred because it is more accurate than estimating Km based on the position of the curve on the plot or by taking the x-axis intercept where V0 = 1/2 Vmax, which can be influenced by experimental error.

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From multiplcation operation, Alex has enough paint to cover 1,000 ft² of his apartment. The true statement is 2 gallons of paint will cover 1068 ft², Alex have enough paint of quantity 2 gallons.

We have Mr. Alex painted his apartment. Area of his apartment'walls = 178 ft²

Quantity of paint used by him to paint his apartment'walls with area 178 ft² =\( \frac{1}{3} \: \: gallons\)

Total quantity of paint used in all

= 2 gallons

We have to check the provide paint is enough or not to cover 1,000 ft² of his apartment. Let the required paint for 1000 ft² be x gallons. Using multiplcation, 1/3 gallons quantity of paint will cover the area of apartment = 178 ft², so, 1 gallons quantity of paint will cover the area of apartment = 178 ×3 ft²= 534 ft²

Now, 2 gallons quantity of paint will cover the area of apartment = 2× 534 ft² = 1068 ft²> 1000 ft²

But he wants to paint 1000 ft² of his apartment in 2 gallons quantity (x=1.9 gal ). So, he has enough paint to paint his apartment.

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Complete question:

The above figure complete the question.

Alex painted 178 ft2 of his apartment’s walls with 1/3 gallon of paint. He has 2 gallons of paint in all. If he wants to cover 1,000 ft2 of his apartment, does he have enough paint? Complete a true statement

No. of children in lamb, chicken, duck, and turkey category is 66, 24, 18 and 12 respectively.

Percentage is the value per hundredth.

According to the given question a survey was carried out among 120 school children looked at which type of meat they preferred. 55% said they preferred lamb,20% said they preferred chicken, 15% preferred duck and 10% turkey and we have to calculate no. of children in each category.

55% said they preferred lamb, So the no. of students i this category is

= (55/100)×120

= 66 children.

20% said they preferred chicken, So the no. of children in this category is

= (20/100)×120

= 24 children.

15% said they preferred duck, So the no. of children in this category is

= (15/100)×120

= 18 children.

10% said they preferred turkey, So the no. of children in this category is

= (10/100)×120

= 12 children.

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Answer:

y - 9 = -18/13(x + 5)

Step-by-step explanation:

Answer:

The tower is 113 meters.

Step-by-step explanation:

We are given a pole and a tower that both create a shadow.

Hence, the figures made are triangles.

If you draw the figure (attached to this response), you can see the two triangles are similar triangles.

⭐What are similar triangles?

The length of the height of the pole (3.2) corresponds to the length of the height of the tower (x).

The length of the shadow of the pole (1.32) corresponds to the length of the shadow of the tower (46.75).

Therefore, our two ratios are:

\(\frac{3.2}{x}\) and \(\frac{1.32}{46.75}\)

A proportion is when you set two ratios equal to each other:

\(\frac{3.2}{x} = \frac{1.32}{46.75}\)

To solve for x, cross multiply by multiplying the opposite parts of the fraction together.

\(\frac{3.2}{x} = \frac{1.32}{46.75}\\46.75(3.2) = 1.32x\\149.6 = 1.32x\\\\113 = x\)

∴ The tower is 113 meters tall!

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Answer:

Answer is D.)

6x3 - 2x2 - 11x + 4

The statement ''the shape of a sampling distribution of sample means that follows the requirements of the central limit theorem will be approximately bell-shaped.'' is true. The statement ''A sampling distribution of sample means has a mean, μ /√n 1to.'' is false.

(a) According to the central limit theorem, when the sample size is sufficiently large, the sampling distribution of sample means will approximate a bell-shaped distribution, regardless of the shape of the population from which the samples are drawn. This is one of the key properties of the central limit theorem.

(b) The correct formula for the mean of a sampling distribution of sample means is μ, not μ/√n. The mean of the sampling distribution of sample means is equal to the population mean (μ). The formula μ/√n is used to calculate the standard deviation (σ) of the sampling distribution, not the mean.

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Answer:

The answer is 10 5/8

Step-by-step explanation:

Answer:

10 and5/8 cups

Step-by-step explanation:

4 and 4/1 cups for 10x12 cookies

17/4 cups for 120 cookies

34/8 cups for 120 cookies

17/8 cups for 60 cookies

we need to find 25 x 12 cookies = 300 = 120+120+60

17/8 + 34/8 +34/8 =85/8 =10and 5/8 cups

The percentage of all patients who took the test and had a false positive result will be 35%. Then the correct option is D.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

Lyme illness is a disease brought about by microscopic organisms. A test for Lyme infection might be impacted by different prescriptions and ailments. The testing results are summed up in the table.

                                      Tested positive      Tested negative     Row Totals

Has Lyme disease                  53%                         17%                     70%

Doesnt have Lyme disease    12%                         18%                     30%

Column Totals                         65%                        35%                    100%

The level of all patients who stepped through the examination and had a misleading positive outcome will be 35%. Then, at that point, the right choice is D.

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Answer:

8/5

Step-by-step explanation:

When we  have two points , we can use the slope formula

m = ( y2-y1)/ ( x2-x1)

    = ( 9-1)/(0--5)

    (9-1)/(0+5)

    8/5

Answer:

The answer is

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-5,1) and (0,9)

The slope is

\(m = \frac{9 - 1}{0 + 5} = \frac{8}{5} \\ \)

We have the final answer as

\( \frac{8}{5} \\ \)

Hope this helps you

By answering the presented question, we may conclude that As a result, the median remains unchanged.

The mean of a dataset is the sum of all values divided by the total number of values; this is also known as the arithmetic mean (as opposed to the geometric mean). This is the most often used measure of central tendency, sometimes known as the "mean." Merely dividing the entire number of values in the dataset by the sum of those values provides this result. Calculations may be performed using both raw data and data that has been compiled into frequency tables. The average of a number is referred to as its average. It is simple to calculate: Divide the total number of digits by the number of digits. the sum divided by the count.

(a) To get the mean of the original data set, add all of the values and divide by the total number of values:

Mean = (360 + 386 + 483 + 526 + 527 + 560 + 791) / 7 = 514

When we alter the value of 791 to 574, the new total is:

360 + 386 + 483 + 526 + 527 + 560 + 574 = 3416

As a result, the new mean is:

Mean = 3416 / 7 = 488

As a result, the mean falls by 26.

(b)

If we change 791 to 574, the resulting data set is as follows:

360, 386, 483, 526, 527, 560, 574

As we sort this data set from least to greatest, the median remains the fourth number (526).

As a result, the median remains unchanged.

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