Show that a = n, where n is an integer.
What is the value of n?

The required distance between the two given cities using the distance formula is 93 miles.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.

The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

So, we have the points:

(53, 17) and (123, 78)

Distance formula:

d = √(x2-x1)² + (y2-y1)²

Now, calculate as follows:

d = √(x2-x1)² + (y2-y1)²

d = √(123-53)² + (78-17)²

d = √(70)² + (61)²

d = √(4,900) + (3,721)

d = √8,621

d = 92.84

Rounding off: 93 miles

Therefore, the required distance between the two given cities using the distance formula is 93 miles.

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The volume of the solid is -30π cubic units

The volume of the solid obtained by rotating the region about the x-axis is given by the formula:

V = π * ∫[a,b] (R^2 - (x-c)^2) dx

Where:

a = lower limit of x-coordinate of the region

b = upper limit of x-coordinate of the region

c = axis of rotation

R = distance from the x-axis to the boundary of the region

For the given region, a = 0, b = 10, c = 10, and R = 2.

So the volume of the solid is:

V = π * ∫[0,10] (2^2 - (x-10)^2) dx

= π * ∫[0,10] (4 - (x-10)^2) dx

= π * [2x - (x-10)^2/2 + C] evaluated at x=10 and x=0

= π * [20 - 100/2 + C - 0]

= π * (20 - 50 + C)

= π * (-30 + C)

= π * (-30) = -30π cubic units.

Therefore, the volume of the solid is -30π cubic units

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The limit of a constant function is equal to the constant. The limit of a linear function is equal to the number x is approaching.

A limit is defined as a value that a function approaches the output for the given input values.

Limit of a constant :-

We know that the limit of a function exists, only and only if the left-hand limit (LHL) and the right-hand limit (RHL) exists and are equal to one another. And, the value of the limit of that function is equal to the common value, LHL = RHL = f(x).

We need to find the limit of a constant. So, let us assume a function, f(x) = c, where c is a constant. We are assuming that we need to find the limit of this constant function at x = a, i.e. we need to find the value of

[tex]\lim_{x \to \ a} f(x)[/tex]

Plot the graph, y = c, (attached)

Let us calculate the left hand limit first.

LHL = [tex]\lim_{x \to \ -a} f(x)[/tex]

We can see that at x = -a, the value of f(x) is c.

LHL = c.....(i)

Similarly,

For right-hand limit,

We have at x = +a, the value of f(x) is c.

RHL = c....(ii)

Also, Also, the value of our function at a, i.e., f(a) = c

Thus, by equation (i), (ii) and (iii), we can say that

[tex]\lim_{x \to \ a} f(x) = c[/tex]

Hence, we can now say that the limit of any constant is the same constant.

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Answer:The probability of a female client choosing health insurance is 65%, and 60% of the company's clients are female, so the probability of choosing health insurance is:

P(health insurance) = 0.65 * 0.60 = 0.39

Therefore, the probability that a health insurance contract is chosen is 0.39.

Step-by-step explanation:

The probability of a female client choosing health insurance is 65%, and 60% of the company's clients are female, so the probability of choosing health insurance is:

P(health insurance) = 0.65 * 0.60 = 0.39

Therefore, the probability that a health insurance contract is chosen is 0.39.

5 STAR AND THANK ME PLS :))

Sample: A sample of 56 fish from a randomly selected Florida lake.

Variable: Mean mercury level in 56 fish from a randomly selected Florida lake

Type of variable: quantitative-discrete

Mean mercury level in fish of all Florida lakes: Parameter of interest

Statistic that will be used: Mean (arithmetic average) of the mercury levels in the sample of 56 fish from the lake.

The sample of 56 fish from a randomly selected Florida lake represents a portion of the population of fish in all Florida lakes. The mean mercury level in these 56 fish represents a statistic, which is an estimate of the population parameter, the mean mercury level in fish of all Florida lakes.

The mean (arithmetic average) is used as the statistic because it summarizes the data by finding the central tendency of the mercury levels in the sample of 56 fish. It is a suitable measure to describe the typical mercury level in the fish from the lake because it takes into account all the observations in the sample.

Since mercury levels are measured in numerical values, the variable "mean mercury level" is quantitative. Since it is a continuous measurement, it is also a continuous quantitative variable.

In summary, the sample and the mean mercury level in the sample of 56 fish are used to make inferences about the population and its parameter, the mean mercury level in fish of all Florida lakes. The mean is used as the statistic to summarize the data and describe the central tendency of the mercury levels in the sample.

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The correct answer is d. dp/dt = 1/1200 P (500-P).

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period it is commonly used mathematics physics economic and other discipline to make operate of vijay process is a caring rate of changing also known as velocity, derivative or slope.

This differential equation describes the rate of change of the number of people entering a movie theater. It states that the rate of change (dp/dt) is equal to the product of 1/1200 and the current number of people (p) in the theater, multiplied by the difference between the capacity of the theater (500) and the current number of people (p). This equation indicates that the rate of change of people entering the theater is proportional to the difference between the capacity and the current number of people.

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The probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice is approximately 0.5949 (rounded off to third decimal place).

To find the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice, we need to find the cumulative distribution function (CDF) of a normal distribution with a mean of 500 and standard deviation 4.

Using the Z-score formula, we can calculate the Z-score for 499 ml of juice: (499-500)/4 = -0.25

Next, we use a standard normal table to find the probability of a Z-score less than -0.25, which is 0.4051.

Finally, we use the CDF formula for a normal distribution to find the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice:

P(X < 499) = 1 - P(X >= 499) = 1 - 0.4051 = 0.5949

Therefore, the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice is approximately 0.5949 (rounded off to the third decimal place).

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The output voltage, in millivolts (mV), for the circuit would be = 1,350 millivolts.

An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.

The output voltage of an amplifier= input voltage × gains.

Where;

input voltage = 45 mV

The gain = 30

Therefore the output voltage= 45×30 = 1350millivolts.

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$150 each month

Step-by-step explanation:

1 year=12 months

$1800/12

= $150 each month

Answer:

$150 each month

Step-by-step explanation:

Step 1: take the amount of money she donates in a year and divide it by 12, because there are 12 months in a year. Dividing 1,800 by 12 will tell you how much money she donates each month.

[tex]\frac{1,800}{12}= 150[/tex]

Answer:

x = 4cm

Step-by-step explanation:

If the triangle is equilateral, then we already know one of the sides has a length of 3+5 (8).

This, therefore, means the 2 other sides' lengths are also equal to eight, which means all we need to do to find x is subtract 4 from 8, which gives us 4.

Hope this helps

Answer:

[tex]x=\dfrac{20}{3}\; \sf cm[/tex]

Step-by-step explanation:

If a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally.

Applying the side-splitter theorem:

[tex]\implies \dfrac{3}{5}=\dfrac{4}{x}[/tex]

Cross multiply:

[tex]\implies 3 \cdot x=4 \cdot 5[/tex]

[tex]\implies 3x=20[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3}=\dfrac{20}{3}[/tex]

[tex]\implies x=\dfrac{20}{3}[/tex]

Therefore, the value of x is ²⁰/₃ cm

Answer:

This is the equation of the normal line at the point (2, 1) on the ellipse (x^2)/4 + y^2 = 2.

Step-by-step explanation:

The equation of the ellipse is (x^2)/4 + y^2 = 2. To find the equation of the normal line at the point (2, 1), we first need to find the slope of the tangent line at that point. To do this, we can use the formula for the slope of a tangent line:

slope = -(d/dx)(f(x)) / (d/dy)(f(y))

Where f(x) and f(y) are the equations of the ellipse.

So,

slope = -(x/2)/y = -x/2y

Now we can substitute the point (2, 1) into the equation for the slope:

slope = -(2/2)/1 = -1

We know that the slope of the normal line is the negative reciprocal of the slope of the tangent line, so the slope of the normal line is 1.

To find the equation of the normal line, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Where (x1, y1) is the point on the line and m is the slope.

So,

y - 1 = 1(x - 2)

Simplifying, we get:

y = x - 1

This is the equation of the normal line at the point (2, 1) on the ellipse (x^2)/4 + y^2 = 2.

Answer: Min=0.02

Q1=0.037037

Med = 0.037037

Q3 = 0.346790

Max = 346

Step-by-step explanation:

To convert the numbers to decimal, we can divide the number before the slash by the number after the slash. So for example, 1/27 becomes 0.037037.

After converting the numbers to decimal and arranging them in ascending order, we get:

0.02, 0.037037, 0.03448, 0.040816, 0.346790, 346

To find the Q1, median (Med), Q3, and other measures of central tendency and spread for this list of numbers, we first need to order the numbers in ascending order:

0.02, 0.03448, 0.037037, 0.040816, 0.346790, 346

Q1 is the value that separates the lowest 25% of the data from the rest of the data. To find Q1, we need to find the median of the lower half of the data set. Since there are 6 numbers in the set and Q1 is the middle value of the lower half, Q1 would be the 3rd number in the ordered set, which is 0.03448.

Med is the middle value of the data set. Since there are 6 numbers in the set, the median would be the 3rd and 4th numbers, which are 0.03448 and 0.037037.

Q3 is the value that separates the highest 25% of the data from the rest of the data. To find Q3, we need to find the median of the upper half of the data set. Since there are 6 numbers in the set and Q3 is the middle value of the upper half, Q3 would be the 5th number in the ordered set, which is 0.346790.

Min is the smallest value of the dataset, which is 0.02

Max is the largest value of the dataset, which is 346

Answer:

1st blank = 45

2nd blank = 90

Step-by-step explanation:

this is an quadratic sequence. (an^2 + bn + c)

use of the formulas

2a = (_)

3a + b = (_)

a + b + c = (_)

The number in scientific notation is 9.2 × 10^-7.

From the question, we have the following parameters that can be used in our computation:

Number = .00000092

The number of points from the initial position to a point between 9 and 2 is -7

This means that the coefficient is 9.2 and the power of ten is -7

So, we have

9.2 × 10^-7.

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Answer:

10^(-7)

Step-by-step explanation:

put first non-zero number, then decimal, then rest of numbers as so

9.2

multiply by +/- depending on where decimal is

9.2*10^(-7)

so 10^(-7)

The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i

What is Quadratic Equation ?

Quadratic equation can be defined as the equation in which it is in the form of ax^2 + bx + c = 0

where c is a constant.

Given equations,

x^2 - 2x +3 = 0

so, we know that

the roots of a quadratic equation

= (- b + (√ b^2 - 4ac ))  / 2a , (- b - (√ b^2 - 4ac ))  / 2a

so,

here a = 1 b = -2 c = 3

by substituting the given values,

we get,

=  2+ (√ 4 - 4*1*3 ) / 2  ,  2- (√ 4 - 4*1*3 ) / 2

= 2+ (√-8)  / 2 , 2- (√-8)  / 2

= 2+8i / 2 , 2-8i / 2

= 1 + 4i , 1- 4i

Hence, The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i

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Answer: The acceleration of the stuntman is given by the second derivative of the height function, which is:

h''(t) = d²h/dt² = (-2 * 2 * t * 1000 + 1000 * -2) = -4000t + 1000

So, the acceleration is -4000t + 1000 ft/sec².

Step-by-step explanation:

The random variable's pdf is f(x) = (3/8) x^2 , x ∈ [0, 2].

Finding the normalizing constant that equals the integral of the pdf over the support of the random variable yields the constant in the pdf (probability density function).

The random variable's support is the interval [0, 2]. The normalizing constant can be calculated as follows:

∫_0^2 x^2 dx = [x^3/3]

_0^2 = (8/3) - (0) = 8/3

So, in the pdf, the constant is 1/(8/3) = 3/8, rounded to the second decimal place.

As a result, the random variable's pdf is:

f(x) = (3/8) x^2 , x ∈ [0, 2].

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Answer:

>

Step-by-step explanation:

3^3*3^-2  ?  3^2*3^-3

27*1/9  ?  9*1/27

3  >  1/3

Answer:

3^3 (times)3^-2 < 3^2 (times) 3^-3

Step-by-step explanation:

3^3 (times)3^-2

27 (times) -9

=-243

3^2 (times) 3^-3

9(times)27

=243

Complementary angles add up to 90°, write an equation using this knowledge and the information provided in the question:

66°+x° = 90°

Subtract 66° from both sides:

x° = 24°

Answer:

300

Step-by-step explanation:

do 20 times 15 and you get 300 length times width = area

Answer:

300

Step-by-step explanation:

First of all, a square's side lengths must be the same for it to be correctly labeled as a square.

The quadrilateral we need to find the area for here is a rectangle.

The area of a rectangle is defined as length × width. So, to answer this question, all we need to do is multiply the given dimensions.

20 × 15

= (2 + 10) × 15

= (2 × 15) + (10 × 15)

= 30 + 150

= 300

The pattern in the following expressions is of square of numbers.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

In given expressions, In divisor the numerator and denominator are square of numerator and denominator in the dividend.

e.g. in (3/5)/(9/25)       9=3^2 and 25=^2

Hence,

            The pattern in the following expressions is of square of numbers.

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In the year 1998, the total average credit card debt for a U.S. household was approximately 6920 dollars.

As per the data given in the questions,

We have,

The expression for calculating the approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995 is: 410t+5690

So, first we will calculate the value of t

As we have in the year 1998, t = 1998 - 1995 = 3.

So, for determining the value of the total average credit card debt in a u.s. household, we will simply plug in this value into the expression,

Thus, will get it as

410 * 3 + 5690

= 1230 + 5690

= 6920

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The value of H^ prime (17) will be 17

At H'(t) = 0 time t, for 9 ≤ t ≤ 23, the model predicts that the number of people in the park is a maximum.

a) To find the number of people who have entered the park by 5:00 P.M. (t = 17),

we need to find the definite integral of the function E(t) from 0 to 17.

b) The total amount of money collected from admissions to the park on the given day is the sum of the money collected before 5:00 P.M. and the money collected after 5:00 P.M.

We can find this by finding the definite integral of the function 15600/(t^2 - 24t + 160) for t from 0 to 17,

Now finding the definite integral of the function

11*9890/(t^2 - 38t + 370) for t from 17 to 23.

c) H(t) represents the number of people in the park at time t. H'(t) represents the rate at which the number of people in the park is changing at time t.

H(17) = 3725 means that at 5:00 P.M. there are 3725 people in the park.

H'(17) can be found by finding the derivative of the function H(t) at t = 17.

d) To find the time t at which the model predicts that the number of people in the park is a maximum, we need to find the maximum value of H(t) for 9 ≤ t ≤ 23.

This can be done by finding the derivative of H(t), setting it equal to 0, and solving for t.

The value of t at which H'(t) = 0 will correspond to the maximum value of H(t).

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Answer:

Step-by-step explanation:

#1 - (−3,9)

#2 - (−∞,−7) and also( −3,∞)

we could go ahead and check its slope and so forth, OR we can just take a peek that the y-coordinates are the same -5, hmmmm well, hell that's just a horizontal line, Check the picture below.

Probability is a measure of the likelihood that a specific event will occur in a random experiment.

What is the Probability?

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

In other words, the probability is a number that represents the chance or chance of an event occurring out of all possible outcomes.

It is expressed as a fraction, decimal, or percentage.

For example, if there is a 50% chance of rain, this means that the probability of rain is 0.5 or 1/2.

Probability is important in decision-making, risk assessment, and mathematical modeling. It helps to quantify uncertainty and provides a way to assess the likelihood of different outcomes.

Hence, Probability is a measure of the likelihood that a specific event will occur in a random experiment.

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The number of miles that the business person can travel  on the $110 is; 290.68 miles

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The daily rate of $37.33 can be said to be the  y-intercept.

While 25 cents or $0.25 can be said to be the slope.

Thus, the equation of the line formed is;

y = 0.25x + 37.33

At a cost of $110, the number of miles is;

110 = 0.25x + 37.33

0.25x = 110 - 37.33

0.25x = 72.67

x = 72.67/0.25

x = 290.68 miles

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Answer:

22 in

Step-by-step explanation:

It travels 35/60 ths of the complete circumference of a circle with r =6 in

diameter = 12     circumference = pi * d

35/ 60  * pi * 12 =  ~22 inches

Answer:

I'm not exactly sure, but I'm positive that it's 60 degrees.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

90 = 30 + (4x)

60 = 4x

x = 60/4 = 15

30° and (4x)° must add up to 90° because they are complementary angles