The distance between City A and City B is 500 miles. A length of 1.5 feet represents this distance on a certain wall map. City C and City D are 2.1 feet apart on this map. What is the actual distance between City C and City​ D?

Answer:

(3)(x)(z)

Step-by-step explanation:

The numeric value of the expression is given as follows:

[f(x + h) - f(x)]/h = 5h + 10x + 6.

To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is given as follows:

f(x) = 5x² - 6x + 1.

The numeric value at x = x + h is given as follows:

f(x + h) = 5(x + h)² - 6(x + h) + 1

f(x + h) = 5(x² + 2xh + h²) - 6x + 6h + 1

f(x + h) = 5x² + 10xh + 5h² - 6x + 6h + 1

Hence:

f(x + h) - f(x) = 5x² + 10xh + 5h² - 6x + 6h + 1 - 5x² + 6x + 1

f(x + h) - f(x) = 10xh + 5h² + 6h

f(x + h) - f(x) = h(5h + 10x + 6).

Simplifying by h, we have that:

[f(x + h) - f(x)]/h = 5h + 10x + 6.

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Answer:

56.52mm

Step-by-step explanation:

If the diameter is 18, the radius is 9.

The formula for circumference is c=2πr

so, 2*3.14*9=56.52

56.52mm

There are 5,642 fans at a concert. If there are 6 seats in each row, the  there are 940 rows each.

Numbers are mathematical objects used for counting, measuring and marking. The original examples are the natural numbers 1, 2, 3, 4, etc. Numbers can be represented by number words. More generally, individual numbers can be represented by symbols, called numerals; for example, "5" is the number representing the number five. Since only relatively few symbols can be memorized, base numbers are usually organized into a number system, which is an organized way of representing any number.

The most common numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of ten basic numeral symbols, called numerals. In addition to being used for counting and measuring, numbers are often used for labels (like phone numbers), orders (like serial numbers), and codes (like ISBNs) . In common usage, a number is not clearly distinguishable from the number it represents.

According to the question:

Number of chairs = 6 and

Number of rows =x

capacity of auditorium =  Number of chairs × Number of rows

⇒ 5642           = 6 × x

⇒ 6x = 5642

⇒ x = 5642/6

⇒ x = 940

round term = 940

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Answer: $2,750

Step-by-step explanation:

Answer:

Add 3

Step-by-step explanation:

The pattern provided can be obtained by adding a constant number to the previous term. The common number is 3 because each term is 3 more than the previous term.

Therefore, you can add 3 to the previous term to get the next term.

"To solve this problem, we can use the Law of Cosines. Let's call the distance the pilot travels before the course correction d1 and the distance she travels after the course correction d2. We want to find the distance between her starting position and ending position, which we can call D.

First, let's find d1:

d1 = (720 mph) * (90 min / 60 min) = 1080 miles

Next, let's find d2:

d2 = (720 mph) * (100 min / 60 min) = 1200 miles

Now we can use the Law of Cosines:

D² = d1² + d2² - 2d1d2*cos(20°)

D² = 1080² + 1200² - 210801200*cos(20°)

D ≈ 1169 miles

Therefore, the pilot is approximately 1169 miles from her starting position." (ChatGPT, 2023)

Answer: 15, 18, 21 (next three terms), Rule: Skip counting by 3

First calculate the common difference between the terms, If [tex]a_{1}, a_{2}, a_{3}, a_{4}.....[/tex] are in sequence, the common difference is calculated by [tex](a_{2} -a_{1}), (a_{3} -a_{2}), (a_{4} -a_{3}) .......[/tex]

Since, the common difference are equal so its clear that the given sequence is an Arithmetic Expression.

The nth term of the AP is an  = a + (n-1)*d

1. Given: 3, 6, 9, 12, .....

  Answer: 15, 18, 21 (next three terms)

  Rule: Skip counting by 3

2. Given: 3, 5, 7, 9, .....

  Answer: 11, 13, 15 (next three terms)

  Rule: Skip counting by 1

3. Given: a, (a+b), (a+2b),.....

  Answer: (a+3b), (a+4b), (a+5b) (next three terms)

  Rule: nth term = a+(n-1)*b = a+nb-b

  if we need 4th term, put n=4 so that 4th term= a+4b-b = (a+3b)

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Answer:

[tex]\boxed{k=\frac{p}{r \ s} }[/tex]

Second option is correct.

Step-by-step explanation:

We have been given that p varies jointly with r and s.

Thus, we can write it mathematically as

[tex]p=krs[/tex]

Here, k is the constant of variation.

Now, we have to find the value of k.

Divide the above equation by rs

[tex]\dfrac{p}{r \ s}=\dfrac{kr\ s}{rs}[/tex]

[tex]k=\dfrac{p}{r s}[/tex]

Hence, the value of k is [tex]k=\dfrac{p}{r s}[/tex]

Second option is correct.

Answer:

B

Step-by-step explanation:

edge 23

The length of JL can be found by subtracting the length of ML from the sum of LK and LN. Therefore, JL = 28 + 16 - 12 = 32.

To find the length of JL, first we can add the lengths of LK and LN. LK = 28 and LN = 16, so 28 + 16 = 44. Then, we can subtract the length of ML from the sum of LK and LN. ML = 12, so 44 - 12 = 32. Therefore, JL = 32.

This can be done by visualizing the diagram. The length of JL can be found by adding the lengths of LK and LN, which can be seen as the two sides of the right triangle that form the line MN. Then, the length of ML can be subtracted from the sum of LK and LN to get the length of JL. This is because the length of JL is equal to the length of LK plus the length of LN minus the length of ML.

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The numerical coefficient of  [tex]\frac{2b}{3}[/tex]   is [tex]\frac{2}{3}[/tex] . So here we know how to find numeric coefficient.

A numerical coefficient is defined as a fixed (stable) number that is multiplied to a variable.

When an algebraic expression consists of several (various) parts, each part that is added called a term. The numerical part of a term is called as its numerical coefficient (or coefficient).

Variable, It is a symbol that represents (means) a mathematical object. A variable may represent(mean) a number, a matrix, a function, a vector, the argument of a set, a function, or an element of a set.

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well, 2 and 1/2 is just 2 + 1/2 or just 2.5, so 2.5%.

[tex]~~~~~~ \stackrel{ \textit{\LARGE 8 years} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$250\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (250)(0.025)(8) \implies I = 50[/tex]

how about after 1 year?  well, we simply set t = 1, so (250)(0.025)(1) = 6.25.

would the interest for t = 2 be the same as for t = 1, if t = 2 is calculated, anyhow, the wording is a bit poor, let me reword it.

after the 1st year, she has an accumulated amount of 250 + 6.25 = 256.25.

now, if for the 2nd year we use the same 2.5% rate BUT we use the accumulated amount of $256.25 to get the interest, instead of the initial $250, will they be the same?

well, hell no, because (250)(0.025)(2) using the inital amount

is not the same as (256.25)(0.025)(2).

bear in mind that simple interest is calculated for each year using the initial amount or deposit, not the accumulated amount thus far.

Answer:

add 3

Step-by-step explanation:

adding 3 to each number for next erm

By making linear equations for given situation, the vendor sold 34 hot dogs and 84 sodas at the football game.

What is a linear equation, exactly?

A linear equation is an algebraic equation in which each term a constant or variable. In other words, a linear equation is an equation of the form:

y = mx + b

where y and x are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).

Now,

Let x be the variable or number of hot dogs sold.

Then, according to the problem, the number of sodas sold is 50 more than the number of hot dogs sold. Therefore, the number of sodas sold can be represented as (x + 50).

We know that the total number of sodas and hot dogs sold is 118, so we can write an equation:

x + (x + 50) = 118

Simplifying and solving for x:

2x + 50 = 118

2x = 68

x = 34

Therefore, the number of hot dogs sold is 34, and the number of sodas sold is (x + 50) = 84.

So, the vendor sold 34 hot dogs and 84 sodas at the football game.

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Answer:

∠ 6 = 59°

Step-by-step explanation:

∠ 3 and ∠ 8 are same- side interior angles and sum to 180° , that is

∠ 3 + ∠ 8 = 180°

121° + ∠ 8 = 180° ( subtract 121° from both sides )

∠ 8 = 59°

∠ 8 and ∠ 6 are vertically opposite angles and are congruent , then

∠ 6 = 59°

Answer:

The coordinates are (-2, 4)

The last option

Step-by-step explanation:

When you rotate 90 degrees clockwise, the coordinates change from (x,y) to (y, -x) so you just substitute the numbers to get the answer.

Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.

The chance that a particular event will οccur is quantified by prοbability. It is a number between 0 and 1, where 0 denοtes that the event is hypοthetical and 1 denοtes that it will undοubtedly οccur. The number οf successful results multiplied by the entire number οf pοssible οutcοmes is used tο calculate an event's prοbability. Tο put it anοther way, prοbability is a way tο express the likelihοοd οf an event οccurring and tο quantify uncertainty.

given:

we can determine the likelihοοd οf receiving twο sοcks οf the same cοlοr.

We can select twο sοcks οf the same hue in any οf the fοllοwing ways:

In ₃C₂ = 3 οptiοns, we can select οur 2 gray sοcks.

There are ₃C₂ = 3 different methοds tο select 2 black sοcks.

Therefοre, there are a tοtal οf 3+3=6 methοds in which we can select 2 sοcks οf the same cοlοr.

There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.

The likelihοοd οf receiving twο sοcks οf the same cοlοr is as fοllοws:

6/15 = 2/5

Thus, the respοnse is c) 2/5.

b) The likelihοοd οf receiving twο pairs οf gray hοsiery is:

There are 3 οptiοns tο chοοse 2 pairs οf gray sοcks (₃C₂ = 3).

There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.

Cοnsequently, the likelihοοd οf receiving twο pairs οf gray hοsiery is:

3/15 = 1/5

Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.

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Note that where the above conditions exists with regard to the geometric ratios, the sum of the antecedents is approximately 445.31.

Let the three continuous geometric ratios be a, ar, and ar^2, where a is the first term and r is the common ratio. Then the equality can be written as:

a/ar + ar/ar² + ar² = 3/4

Simplifying this equation, we get:

1/r + r + r² = 3/4

Multiplying both sides by 4r², we get:

4r + 4r³ + 4r⁴ = 3r²

Rearranging, we get:

4r⁴ + 3r² - 4r = 0

We can factor this equation as:

r(4r³ - 4r² + 3) = 0

Since r cannot be zero, we must solve the cubic equation:

4r³ - 4r² + 3 = 0

Using a numerical method or a computer program, we can find that one real root of this equation is approximately 0.8202.

Now that we know the value of r, we can use the difference between the largest and minor consequent to find the value of a. The largest consequent is ar², and the minor consequent is a, so we have:

ar² - a = 120

Substituting r = 0.8202, we get:

a(0.8202)² - a = 120

Simplifying, we get:

a = 120 / (0.6721)

a ≈ 178.63

Finally, we can calculate the sum of the antecedents:

a + ar + ar² = 178.63 + (178.63)(0.8202) + (178.63)(0.8202)²

Summing these terms, we get:

a + ar + ar² ≈ 445.31

Therefore, the sum of the antecedents is approximately 445.31

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Translation:

If the sum of the ratios of an equality of 3 continuous geometric ratios is 3/4, calculate the sum of antecedents. Consider that the difference between the largest and minor consequent is 120

Answer:

(x+1)(x-6)

Step-by-step explanation:

two number that times to make -6 and add to make-5

these are : -6 and +1

(x+1)(x-6)

when u expand it

x^2-6x+x-6

=x^2-5x-6

Equation for the line passing through the point (-3, -1) is:

c. y = -1

Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.

Now in the question here,

The line passes through the point (-3, -1).

So, the equation that satisfies the point is: y = -1.

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The optimal number of TVs to sell in order to achieve the highest profit are 24 and 48, respectively

Given the question, the objective function can be stated as follows.

P(n, m) = 175b + 205m

The given values for the constraints and the result of evaluating them are provided as

After analyzing the above values, we have identified the highest value as

Maximum = 14040

These values are at

b = 24 and m = 48

Hence, the number of TV to be sold are 24 and 48, respectively

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The total cost of the camera with sales tax included is $976.68

The listed  price of the camera = $891.95

The sales tax rate = 9.5%

The amount of tax = The listed  price of camera × (The sales tax rate / 100)

Substitute the values in the equation

The amount tax = 722.95 × (9.5 / 100)

Divide the terms first

= 891.95 × 0.095

Multiply the terms

= $84.735

The cost of the camera including tax = The listed  price of camera + The amount of tax

Substitute the values in the equation

= 891.95 +84.735

= $976.68

Hence, the total cost of the camera with sales tax included is $976.68

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Accοrding the given questiοn 0.16 is 0.4 Percentage οr % οf 40

A percentage is a number οr ratiο that can be expressed as a fractiοn οf 100 in mathematics. If we need tο calculate a percentage οf a number, multiply it by 100 and divide it by the tοtal. Sο, a part per hundred is what the percentage refers tο. Percent means fοr every 100. The symbοl "%" is used tο denοte it.

Percentages have nο dimensiοn. Hence it is called a dimensiοnless number. If we say, 50% οf a number, then it means 50 per cent οf its whοle.

0.4% is equivalent tο 0.4/100 = 0.004 as a decimal.

Tο find οut what number (a) is 0.4% οf 40, we can use the fοllοwing fοrmula:

a = 0.004 x 40

a = 0.16

Therefοre, 0.4% οf 40 is 0.16.

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Therefore , the solution of the given problem of probability comes out to be there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.

The primary goal of the designs inside a practice known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1 can be used to represent chance, with 1 usually representing a range level of certainty and 0 typically representing possibility. A probability diagram shows the chance that a specific event will occur. Just the digits 0% and approximately 100% make up the decimal 1, 0, and 0.

Here,

To resolve this issue, we can use the conventional normal distribution. First, we must standardise the 96 number using the following equation:

=> z = (x - μ) / σ

where the mean is, the standard deviation is, and x is the number we're interested in. When we enter the numbers, we obtain:

=> z = (96 - 85) / 4.6 = 2.3913

The area to the right of z = 2.3913 can then be determined using a calculator or a conventional normal distribution table.

The area to the right of 2.39, according to a standard normal distribution chart, is 0.0084. (rounded to four decimal places).

As a result, there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.

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The operations used here are as follows:

Addition.

Division.

The order of operations is a collection of rules that must be followed in a particular order while solving an equation.

The evaluation of any mathematical expression, which includes arithmetic operations like addition, subtraction, multiplication, and division, is what we mean when we say "operations" in mathematics.

Here in the question,

For the 2nd step,

10 was added on both the sides of the equation.

So, addition was the property used.

For the 4th step,

3 was divided from both the sides of the equation.

So, division was the property used.

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The slope-intercept form of this table is y = 3x - 10.

In Mathematics, the point-slope form of any straight line can be determined by using the following mathematical expression:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex] or y - y₁ = m(x - x₁)

Where:

At point (25, 65), an equation of this line in slope-intercept form can be calculated by using the point-slope form:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

[tex]y - 65 = \frac{(68- 65)}{(26 - 25)}(x - 25)[/tex]

y - 65 = 3(x - 25)

y = 3x - 75 + 65

y = 3x - 10.

In this context, we can reasonably infer and logically deduce that an equation of the line that represents this table in slope-intercept form is y = 3x - 10.

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The correct answer is answer choice- A.

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

See the attached worksheet. The use of a filled or unfilled circle on a number indicates whether that actual number is included (solid circle) or not included (empty circle)  A solid bar between two points telss us these points are all included.  

 -3<x<3 does not have an equality ("=") for ether +3 nor -3.  The the line between those points would be solid (all points are allowed).  Either 3 would be an empty circle.  

Option A seems to have these features.