Find the minimum value of the function f(x) = x² +10.5x + 20 to the nearest
hundredth.

They begin at a distance of 210 feet, hence the distance between them is equal to 210 - 2sx feet

A) Accordingly, if x equals "the number of feet Alan has gone since he started walking toward Victoria," then A) the combined distance (in feet) covered by the two walkers must be 2x, and B) Alan's distance from Victoria must be 210 - 2x.

B) In other words, if Alan and Victoria are walking at the same speed, let's call that speed s, then the total distance each of them has traveled is equal to sx ft (x = the amount of time since they began walking), which equals 2sx ft.

C) They begin at a distance of 210 feet, hence the distance between them is equal to 210 - 2sx feet.

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Answer:

1. Rational

2. False

Step-by-step explanation:

1. You will always get a rational number when you add, subtract, multiply, or divide rational numbers.
2. All whole numbers, integers, and natural numbers are rationals, but not all rational numbers are integers, natural numbers, or whole numbers.
Hope it helps!

Answer:

x = 3/2  or x = -1

Step-by-step explanation:

After putting the first 2 terms together and the second 2 terms together, what needs to be in the middle is; Parenthesis around all 4 terms

Factorization by grouping in algebra simply means that we need to group the terms with common factors before factoring.

Now, some of the steps to take in this regards are;

- From the groups of the given expression a factor can be taken out from each group.

- Factorize each group

- Now take out the factor common to group formed.

Thus, from the above after grouping the terms together, the next thing to be in the middle is to put parentheses around the 4 terms.

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The length of the sides a and b are respectively 19.67 and 20.21 approximately to 2 decimal place, using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

For the triangle ABC, by sine rule;

a/sinA = b/sinB = c/sinC

We first derive the angle A as follows:

75° + 35° + A = 180° {sum of interior angles of a triangle}

A = 180° - 110°

A = 70°

Thus by sine rule;

b/sin75° = 12/sin35°

b = (12× sin75°)/sin35° {cross multiplication}

b = 20.21

a/sin70° = 12/sin35°

a = (12× sin70°)/sin35° {cross multiplication}

a = 19.67

Therefore, the length of the sides a and b are respectively 19.67 and 20.21 approximately to 2 decimal place, using the sine rule.

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The required expected value of the pointer landing on the blue is 9.4 times.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
From the table,
Frequency of blue color = 14
Total outcome = 75

Probability of landing on blue = P(b) = 14 / 75

Now,
The spinner is spun 50 times,
The expected value of the color blue is given as,
E(b) = n × P(b)

E(b) = 50 × 14/75

E(b) = 9.4 times

Thus, the required expected value of the pointer landing on the blue is 9.4 times.

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The original price of the car is $17420

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, a sale price of $13,065, which is 25% less than it sold for when it was new,

We need to find the original price of the vehicle,

Let the original price be x,

x - 25% of x = 13065

x(1-25%) = 13065

x(75/100) = 13065

x = 13065 × 100 / 75

x = 100 × 174.2

x = 17420

Hence, the original price of the car is $17420

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[(x₁ + x₂)/2, (x₁ + x₂)/2] is the formula to find: B. the midpoint.

[(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)] is the formula to find: A. the point that partitions a segment into a ratio of m : n, where m : n is not 1 : 1.

In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.

In Mathematics, a line ratio can be defined as the set of points that partitions a line segment into a ratio of m : n and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

where:

m : n is not 1 : 1.

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The percent increase in the collections is 40%.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %.

Percent increase = (increase in the number of collections / initial collections) x 100

Increase in collections = 14 - 10 = 4

= (4/10) x 100 = 40%

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5. The temperature dropped by 10 - (-24) = 34 degrees.

6. The fish swam down 120 - 52 = 68 meters.

7. The difference between the elevation of the Dead Sea and Lake Assal is (-420) - (-156) = 264 meters.

8. The sum of the temperatures is -10 + 24 - 12 + 8 - 1 = 9 degrees Celsius

A temperature drop refers to a decrease in the temperature from one point to another, for example, from a higher temperature to a lower temperature.

It could then be concluded that the correct answers are 34 degrees, 68 meters, 264 meters, and 9 degrees Celsius respectively.

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The transformation h(x)=3x^2-7 will cause the graph of f(x)=x^2 to stretch vertically by a factor of 3 and shift 7 units downward.

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

f(x) = x^2

h(x) = 3x^2 - 7

This means that

h(x) = 3f(x) - 7

This in other words, the transformation "stretches" the graph of f(x) = x^2 vertically by a factor of 3 and "translates" it vertically by shifting it downward by 7 units.

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Total cost of soda and popcorn for 5 people = $6.00 x 5 = $30.00

Yes, two different expressions to calculate the total cost of the soda and popcorn for Tina and her family are:

Expression 1: Total cost of soda = $2.50 x 5 (5 people) = $12.50

Total cost of popcorn = $3.50 x 5 = $17.50

Total cost of soda and popcorn = $12.50 + $17.50 = $30.00

Expression 2: Total cost of soda and popcorn for one person = $2.50 + $3.50 = $6.00

Total cost of soda and popcorn for 5 people = $6.00 x 5 = $30.00

A ratio is a comparison of two or more values. It is a way of expressing the relationship between two or more quantities in the form of a fraction. The numerator of the fraction represents the first quantity and the denominator represents the second quantity. The ratio can be written in the form of a:b, where a and b are the two quantities being compared.

For example, if you have 4 apples and 2 bananas, the ratio of apples to bananas can be expressed as 4:2 or 2:1. This means that for every 2 bananas, there are 4 apples. Ratios can also be used to compare values of different units, for example, miles to kilometers or pounds to kilograms.

Ratios are widely used in many fields, including finance, cooking, construction, and physics, to compare and express the relationship between different quantities. They provide a simple and intuitive way to compare values and help to make sense of complex data.

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The volume of the cylindrical water cooler is 211.38 gallons. Therefore, option C is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall.

Now, radius = 3/2 =1.5 feet

We know that, the formula to find the volume of a cylinder is πr²h.

Here, 3.14×1.5²×4

= 28.26 cubic feet

In gallons = 28.26×7.48

= 211.38 gallons

Therefore, option C is the correct answer.

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The correct option is C, 211.38. Hope this helps :)

Answer:
The percent increase for airfares from Hartford to Boston is:

(300 - 225)/225 * 100% = 33.333%

If the airline charges an additional $50 baggage fee with the new ticket price, the percent increase from 300 to 350 is:

(350 - 300)/300 *100% = 16.67%

The two expressions for this situation, with one representing the cost per customer and the other representing the average number of customers are:

Cost: 10 + x

Customer: 16 - 2x

Inequality: 160 - 4x - 2x² ≥ 130.

Based on the information provided, we can logically deduce that the amount of money being charged by Noah per buffet is equal to $10. Also, the total number of customers that chose buffet every hour is equal to 16 customers.

For an increase in the cost of buffet by $1, the average number of customers who selected the buffet would decrease by 2 per hour and the minimum revenue per hour is $130.

Therefore, an expression that represents the cost per customer is given by;

Cost: 10 + x

Additionally, an expression that represents the average number of customers;

Customer: 16 - 2x

Lastly, an inequality that would help Noah make the best pricing decisions is as follows;

Revenue = Cost × Customers

(10 + x) × (16 - 2x) ≥ 130

160 - 20x + 16·x - 2x² ≥ 130

160 - 4x - 2x² ≥ 130

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The comparison is

1/3×5/7 < 2/5+4/4

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

1/3×5/7 ⭕️ 2/5+4/4

we solve the quantities one by one

1/3×5/7

= 5/ 21

and, 2/5+4/4

= 28/20

= 7/5

So, 1/3×5/7 ⭕️ 2/5+4/4

5/21 ⭕️ 7/5

25/105 < 174/105.

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The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.

Let P(F) be the prior probability of a sensor fault and P(M|F) be the probability of measurements below 1m given a faulty sensor. Then, the posterior probability of a sensor fault given N consecutive measurements below 1m is given by

P(F|M1 ,M2 ,...,MN )=P(F)P(M1|F)P(M2|F)....P(MN |F)/P(M1 ,M2 ,...,MN )

P(M1 ,M2 ,...,MN ) = P(M1)P(M2)....P(MN) = (1/3)^N

Therefore,

P(F|M1 ,M2 ,...,MN )=P(F)(1/3)^N

For N = 1,2,...,10

P(F|M1 ,M2 ,...,MN ) = 0.01 (1/3)^N

For N = 1, P(F|M1)= 0.01/3

For N = 2, P(F|M1,M2)= 0.01/9

For N = 3, P(F|M1,M2,M3) = 0.01/27

Similarly, for N= 4,5,6,7,8,9,10

P(F|M1,M2,M3,M4,M5,M6,M7,M8,M9,M10) = 0.01/81, 0.01/243, 0.01/729, 0.01/2187, 0.01/6561, 0.01/19683, 0.01/59049 respectively.

The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.

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Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

subscription for 8 months

She paid $28 and Holly wanted to find the price, p

Price for one month is :

=> 28/8

=> $3.5

Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.

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The complete question is "Holly bought a magazine subscription for a year. She paid $27. Holly wanted to find the price, p, of the subscription each month. She created the model shown to help find this price. 27 р |р |р |р |р |р |р |р | Р | Р |р | p What was the price of the subscription each month? F $39.00 G $2.25 H $324.00 3 $22.50​"

The number of chalkboards that the school will be able to give away is 89.

In order to determine how many chalkboards the school can give away, the mathematical operation that would be used is division.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Number of chalkboards the school can give away = total amount the school has to spend / cost of each chalkboard #

$3,293 / $37 = 89

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The solution is, the area of the given figure is 38.6 ft^2.

The area of a trapezoid is found using the formula, A = ½ (a + b) h,

where 'a' and 'b' are the bases (parallel sides) and 'h' is the height .

here, we have,

from the given figure , we get,

the trapezoid's,

parallel sides are, 9 ft. & 7ft.

height = 3.6 ft.

so, area = ½ (a + b) h,

i.e. A = 28.8 ft^2

Again, area of the triangle is,

area = 1/2 * base * height

         = 1/2 * 7* 2.8

         = 9.8

total area = 38.6 ft^2

Hence, The solution is, the area of the given figure is 38.6 ft^2.

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z is the z-score for the desired confidence level. For 95 percent confidence, z = 1.96 and for 99 percent confidence, z = 2.58.

(a) To calculate the 95 percent and 99 percent confidence intervals for u, we can use the formula:

mean ± z*(standard deviation/sqrt(sample size))

Plugging in the values, we get:

95 percent confidence interval: 5.46 ± 1.96*(2.47/sqrt(100)) = 5.46 ± 0.39

99 percent confidence interval: 5.46 ± 2.58*(2.47/sqrt(100)) = 5.46 ± 0.52

(b) For the 95 percent confidence interval, the interval is 5.46 ± 0.39, which means that we can be 95 percent confident that the true mean waiting time u is between 5.07 and 5.85 minutes. Since 6 minutes falls outside this interval, we cannot be 95 percent confident that u is less than 6 minutes.

(c) For the 99 percent confidence interval, the interval is 5.46 ± 0.52, which means that we can be 99 percent confident that the true mean waiting time u is between 4.94 and 5.98 minutes. Since 6 minutes falls outside this interval, we cannot be 99 percent confident that u is less than 6 minutes.

(d) Based on the results of the 95 percent and 99 percent confidence intervals, we can conclude that there is not enough evidence to be confident that the new mean waiting time is less than six minutes.

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1) Completing the square is a good solving option when b is an even number.

2) The discriminant of the quadratic equation y² = x² + 4x + 4 is positive.

What is discriminant?

The discriminant of a polynomial is a number that depends on the coefficients and allows some properties of the roots to be deduced without having to compute them.

1) Completing the square is a good solving option when b is an even number.

Completing the square is a technique used to solve quadratic equations of the form ax² + bx + c = 0 by rewriting the equation as a perfect square. This technique is particularly useful when b is an even number because it makes it easier to recognize the perfect square pattern.

For example, if b = 2, then the equation can be written as ax² + 2x + c = 0. By adding and subtracting the same term, this equation can be rewritten as a(x + 1)² + (c - a) = 0, which is a perfect square. Solving the equation then becomes a matter of finding the square root of the constant term.

If b is an odd number, the equation can still be solved using the completing the square technique, but it may require more steps.

Hence, Completing the square is a good solving option when b is an even number.

2) The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by b² - 4ac. In this case, a = 1, b = 4, and c = 4, so the discriminant is b² - 4ac = 4² - 4 * 1 * 4 = 16 - 16 = 0.

A positive discriminant means that the equation has two real and distinct roots, a negative discriminant means that the equation has two complex roots, and a zero discriminant means that the equation has one real root (a double root).

Hence, The discriminant of the quadratic equation y² = x² + 4x + 4 is positive.

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\textit{we'll be using this one}}{log_a a^x = x}\qquad \qquad a^{log_a x}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 140\\ P=\textit{original amount deposited}\dotfill & \$70\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]140 = 70e^{\frac{r}{100}\cdot 5} \implies \cfrac{140}{70}=e^{\frac{r}{20}}\implies 2=e^{\frac{r}{20}}\implies \log_e(2)=\log_e\left( e^{\frac{r}{20}} \right) \\\\\\ \log_e(2)=\cfrac{r}{20}\implies \ln(2)=\cfrac{r}{20}\implies 20\ln(2)=r\implies \boxed{13.86\approx r}[/tex]

1. The ordered pair (1, 5) is a solution to the system of equations.

2. The ordered pair (-2, 0) is NOT a solution to the system of equations.

To determine if the ordered pair (1, 5) is a solution to the system of equations, we substitute the values into the equations and see if they hold true.

-5(1) + 6(5) = 25

25 = 25 (holds true)

-7(1) + 8(5) = 33

33 = 33 (holds true)

Since both equations hold true for the values of m=1 and n=5, we can conclude that the ordered pair (1, 5) is a solution to the system of equations.

To determine if the ordered pair (-2, 0) is a solution to the system of equations, we substitute the values into the equations and see if they hold true.

8(-2) - 3(0) = -16

-16 = -16 (holds true)

-9(-2) - 2(0) = 50

4 ≠ 50 (does not hold true)

Since one of the equations does not hold true for the values of x=-2 and y=0, we can conclude that the ordered pair (-2, 0) is NOT a solution to the system of equations.

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The lenght of the dotted line in the given diagram is 5.92

The dotted line in the given diagram is the diagonal of the rectangle. The lenght of diagonal can be calculted using phytagoras theorem:

diagonal² = length² + wide²

From the diagram, we know that the wide of the rectangle is 1, however we have no information about the length of the rectangle yet. If we look to the attached triangle, we can know that the lengt of rectangle is actually the hypotenuse of the triangle.

We can find the hypotenuse of the triangle using the phytagoras theorem:

hypotenuse² = base² + height²

hypotenuse² = 3² + 5²

hypotenuse² = 9 + 25

hypotenuse² = 34

We can use the value of squred hypotenuse as the squared length to find the length of the diagonal:

diagonal² = length² + wide²

diagonal² = hypotenuse² + wide²

diagonal² = 34 + (1)²

diagonal² = 35

diagonal = 5.92

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Based on Madison's equation, the y-value is equal to 8.5.

In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).

In order to use the given function to determine the value of y (y-value), we would have to substitute the values of x (x-value or domain) into the function and then evaluate as follows;

y = 0.5x² + 4

y = 0.5(-3)² + 4

y = 0.5(9) + 4

y = 4.5 + 4

y = 8.5.

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12 is the  missing number of the unit rate 36/3=\1.

Two or more expressions with an Equal sign is called as Equation.

Let us consider the missing number be x in the given equation

36/3=x/1

36 and 3 are the multiples of 3 so divide numerator and denominator by 3

36 divided by 3 is equal to twelve

so the value of x is 12

Hence, 12 is the  missing number of the unit rate 36/3=\1.

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The solution is, the expression is => 4*(5-x)

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

let, the number is x.

now, when,

4 is multiplied by the difference of 5 and a number.

so, we get,

the expression is => 4*(5-x)

Hence, The solution is, the expression is => 4*(5-x)

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Answer:

11

Step-by-step explanation:

find ratio of girls to boys

22:11 divide by 11

2:1

2girls and 1boy in every boy makes 11 groups

The number of questions answered correctly on a standardized test and the length of time required to answer a telephone call at a certain real estate office are all numerical (quantitative) variables.

a. The breaking strength of a given type of string. Numerical (quantitative)

b. The hair color of children auditioning for the musical Annie. Attribute (qualitative)

c. The number of stop signs in towns of fewer than 500 people. Numerical (quantitative)

d. Whether or not a faucet is defective. Attribute (qualitative)

e. The number of questions answered correctly on a standardized test. Numerical (quantitative)

f. The length of time required to answer a telephone call at a certain real estate office. Numerical (quantitative)

For example, if a standardized test had 10 questions, and a student answered 7 correctly, the numerical (quantitative) variable for the number of questions answered correctly would be calculated with the formula: 7/10 = 0.7 or 70%. The length of time required to answer a telephone call at a certain real estate office can also be calculated numerically (quantitatively) by taking the total time of the call and dividing it by the number of calls. For instance, if the total time of 10 telephone calls was 80 minutes, the numerical (quantitative) variable for the length of time required to answer a telephone call would be calculated with the formula: 80/10 = 8 minutes.

Based on the examples given, the breaking strength of a given type of string, the number of stop signs in towns of fewer than 500 people, the number of questions answered correctly on a standardized test and the length of time required to answer a telephone call at a certain real estate office are all numerical (quantitative) variables, while the hair color of children auditioning for the musical Annie and whether or not a faucet is defective are attribute (qualitative) variables.

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