Write a quadratic function for the area of the figure. Then, find the area for the given value of x.
x=7
A quadratic function for the area of the figure is A(x)= (Simplify your answer.).

The time take for the object to cool down is 5 minutes.

The temperature of a substance is a measure of its thermal energy and it is important to know how it changes over time.

Heat transfer occurs from hot to cold, meaning that the coffee will transfer heat to the room until both reach thermal equilibrium. The temperature difference between the coffee and the room is

=> 80°C - 25°C = 55°C.

We will use this value to calculate the rate of heat transfer. We know that the final temperature of the coffee will be 45°C, so the temperature difference will become

=> 45°C - 25°C = 20°C.

The time it takes to cool from 80°C to 45°C will depend on the heat transfer rate, which is affected by factors such as the mass of the coffee, the material of the container, and the surrounding environment.

Let us consider that the average heat rate is 60 seconds that is one minute.

Then the time taken for it is calculated as,

=>20 x 60 = 300

So, in minutes 5 minutes.

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The unit digit of the product of 91, 92, 93, ... 99 is 0.

The digit that goes in the place of one in a number is known as the unit digit. i.e. It is the number's rightmost digit. As an illustration, the unit digit for 243 is 3, whereas the unit digit for 39 is 9.

It is easy to identify the unit place digit of the smaller number but when it comes to the numbers raised to the larger power it becomes difficult to identify the same by simple observation. It is when the concept of cyclicity comes into the picture.

The cyclicity concept is based on the fact that every digit in the number has its own repetitive pattern when raised to any specific power. This particular concept makes it easy for the students to find the unit place digit of the larger numbers and that too at much less time. So, let's learn about the cyclicity concept.

For example: - 2² = 4. Here, the unit digit is 4

2³ = 8. Here, the unit digit is 8.

Given:

91 × 92 × 93......×98 × 99

We want to find unit digit of the product of the numbers.

Here two digit is 92 and 95.

If we multiply 92 and 95, we will get zero as unit digit and if we multiply any digit by zero, unit digit always be zero.

So, the product of 92× 95 has zero in unit place.

So, in product of all numbers 91 × 92 × 93......×98 × 99 the unit will be zero. Because when we multiply any number by zero it become zero.

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Each side of the square should be matched with its slope as follows;

Side WX = 1/8.

Side YZ = -8.

In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other. Therefore, we would have to calculate the slope of each side by using this mathematical expression:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Where:

x and y represents the data points or side lengths of a quadrilateral.

For side WX, the slope is given by:

Slope (m) = (3 - 2)/(5 - (-3))

Slope (m) = (3 - 2)/(5 + 3)

Slope (m) = 1/8.

In Mathematics, a condition that must be met for two (2) lines or side lengths to be perpendicular is given by:

m₁ × m₂ = -1

1/8 × m₂ = -1

m₂ = -8

Slope (m₂) = -8

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Persons over the age of 40, African-Americans, people with hypertension or pre-hypertension, and people with diabetes are among these populations. Anyone in these groups should restrict their daily salt consumption to 1,500 mg.

Blood sodium levels should be between 135 and 145 mEq/L (3.10 mg/ml to 3.34 mg/ml). Higher sodium levels are often connected with hypertension. Hypernatremia is defined as a sodium level of 150 mEq/L (3.45 mg/ml) or higher, which is frequently caused by dehydration or ingesting too much salt. On some food labels, the salt amount is the sole information provided. To convert sodium to salt, increase the quantity by 2.5. Then double the salt content per 100g by 100 and multiply by the serving size. For most individuals, the American Heart Association advises no more than 2,300 milligrams (mg) per day, with an optimal limit of no more than 1,500 mg per day.

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The cost of polishing the floor of the square hall is ₹2343.75

The Side of Square Hall = 12.5 m

The cost of polishing the floor per meter sq. = ₹ 15

We have to find the cost of polishing the floor.

First we will calculate the area of floor of the square hall.

Area of a square is defined as the number of square units needed to fill a square. In general, the area is defined as the region occupied inside the boundary of a flat object or 2d figure. The measurement is done in square units, with the standard unit being square meters ([tex]m^{2}[/tex]).

Area of square=[tex](12.5)^2[/tex]

Area of square =[tex]12.5 \times 12.5[/tex]

Area of square =156.25

The area of the floor of Square Hall is 156.25 [tex]\mathrm{~m}^2$[/tex]

Per square meter cost of polishing the floor is ₹15,

To find the cost of polishing the floor of the square hall of area 156.25 sq. m, simply multiply 15 by the area of the floor of the square hall.

Therefore, the cost of polishing,

=15×156025

=2343.75

Therefore, the cost of polishing is ₹2343.75.

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Find the cost of polishing the floor of a square hall at the rate of 15 per meter sq, if each side of the hall is 12.5 m.​

Answer:

y = -3/4x - 1/4.

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Given the slope : -3/4 and y-intercept : -1/4, the equation of the line is y = -3/4x - 1/4.

The probability that player 1 wins m times is [tex]$\frac{m}{n}[/tex].

Assume that the numbers 1,2, ....., and n are randomly given to players.

Consider,

[tex]\Omega & =\{1,2, \ldots, n\} \\[/tex]

[tex]& =\left\{\omega_1, \omega_2, \ldots, \omega_n\right\}[/tex]

Here, player 1 and player 2 compare their numbers.

The one with the largest number wins and compares her number with player 3 and So on...

If all outcomes are equally likely,

[tex]\Omega=\left\{\omega_1, \omega_2, \ldots . ., \omega_n\right\}[/tex]

Then [tex]$\Omega$[/tex] is equiprobable sample space.

The probability of each [tex]$\omega_i$[/tex] is [tex]$\frac{1}{n}[/tex] for i = 1, 2, ..........., n

[tex]$P\left\{w_1\right\}=P\left\{\omega_2\right\}=P\left\{\omega_3\right\}............P\left\{\omega_n\right\} = \frac{1}{n}[/tex]

These numbers are randomly given then it has m Sample points.

Probability = P (player 1 wins m times)

For every subset of numbers chosen uniformly at random all possible permutations of these numbers are equally likely.

[tex]$\Rightarrow P(A)=\frac{1}{n}+\frac{1}{n}+\cdots \cdots+\frac{1}{n} \text { ( mimes) }[/tex]

The number of sample points in A is divided by a number of Sample points in [tex]} \Omega}$[/tex].

[tex]$=\frac{\text { number of sample points in } A}{\text { number of Sample points in } \Omega}[/tex]

[tex]$=\frac{\text { number of favorable cases to event } A}{\text { number of possible cases }}$[/tex]

[tex]$=\frac{m}{n} \\[/tex]

Therefore P(A) = [tex]$\frac{m}{n}[/tex]

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Answer:

This is actually quite simple

Step-by-step explanation:

Divide them both by 20

then add

Your final answer either should be D or A

The combined cost of c dollars is a xπx² + 2πxhb. The volume of the tank will be V = πx²h. Maximum value of V is when c > 2a(2hb).

a. The cost of the base is given by a xπx², and the cost of the curved surface is given by 2πxhb. The combined cost of the base and curved surface is given by:

c = a xπx² + 2πxhb

b. To find the volume of the tank, we can use the formula for the volume of a cylinder:

V = πx²h

Substituting in the expression for c from part (a), we have:

V = πx²h = πx²(c - 2πxhb) / a

c. To find the maximum value of V, we can differentiate with respect to x and set the derivative equal to 0:

dV/dx = 2πx(c/a - 2hb) = 0

Solving for x, we get:

x = (c / 2a) / (2hb)

Since x is the radius of the tank, it must be positive, so we must have c > 2a(2hb) for the maximum value of V to exist.

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The solution set to the inequality (4x-3)(2x-1)20 is x ≤ 1/2 or x ≥ 3/4. Option C

An inequality, is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

(4x-3)(2x-1) ≥ 0

expanding the brackets

8x^2 - 4x - 6x + 3

8x^2 -10x +3

(8x^2 -6x) -(4x+3)

Factoring the common factors

2x(4x-3)-1(4x-3)

(2x-1)(4x-3) ≥ 0

2x-1 ≥ 0

dividing both sides by 2

x≤-1/2

4x-3≥0

Dividing both sides by 4

x≤3/4

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It is true that if v in r3 and v·v = 0, then v is the zero vector.

If v is a vector in R3 (three-dimensional real space) and v·v = 0, then v is the zero vector.

The dot product of a vector with itself, v·v, is equal to the square of the magnitude of the vector, ||v||^2. If v·v = 0, it follows that ||v||^2 = 0, which means that the magnitude of v is 0. In other words, v has a length of 0.

The only vector in R3 with a length of 0 is the zero vector, which is represented by the vector (0, 0, 0). Thus, if v·v = 0, v must be the zero vector.

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The right answer is option B, which is "As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞."

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depended on another quantity.

Here,

First, you must graph all of the supplied points in the table in order to establish the final behavior.

Remember that the behavior of f(x) as x approaches positive and negative infinity is the end behavior of a function.

According to the graph, as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches negative inifinity. In other words, f(x) always approaches negative infinity in any situation.

The correct answer is option B that is "As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞."

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Answer: TRUE

Step-by-step explanation:

For the sake of typing this easier, I'm going to omit using theta however the final answer will have it.

RH:

Knowing that csc = 1/sin, csc² = 1/sin²

LH:

Knowing that cot = cos/sin, cot² = cos²/sin²

Another important trig identity is sin² + cos ² = 1

So therefore you now have:

cos²/sin² + sin² + cos²

Put everything under the same denominator:

cos² + sin²*sin² + cos²*sin² / sin²

= cos² + sin²(sin² + cos²) / sin²

= cos² + sin² (1) / sin²

= 1 * 1 / sin²

= 1 / sin²

Therefore this trig identity is true

The number of each type of books purchased is, 6 mystery and 8 sci-fi

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given  that,

$5 clearance mystery books

And $12 regular-priced science fiction book

Total spent amount = $126

The number of each type of books purchased  = ?

Suppose, the number of clearance mystery books = x

the number of regular-priced science fiction book = y

So it can be written as,

5x + 12y = 126

Here, in question Second condition is missing

So we can took values of x & y from the options,

Let, x = 6 and y = 8

5x6 + 12x8 = 126

It is satisfied the condition

Let, x = 7 and y = 7

5x7 + 12x7  ≠ 126

Similarly, rest options not satisfy the condition

Hence, the number of books 6 mystery and 8 sci-fi

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when interpreting a histogram with a normal curve, it is important to look at the shape of the histogram and compare it to the shape of the normal curve. This can help us determine if the data is normally distributed, identify outliers, and determine the goodness of fit of the data to a normal distribution.

Histograms and normal curves are two commonly used graphical representations of data. A histogram is a bar graph that represents the frequency distribution of a set of continuous data. A normal curve, also known as a Gaussian distribution or Bell curve, is a symmetrical and bell-shaped curve that represents the probability density function of a normally distributed set of data.

When a histogram is superimposed with a normal curve, it allows us to visually compare the distribution of the data with a normal distribution. In this article, we will discuss how to interpret a histogram with a normal curve.

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Answer:

2x-3

Step-by-step explanation:

3/x-4=x-5/x=

first what you need to do  is

3/x-4 so its both a fraction 3/x and 5x and subtraction on both sides makes it easer for us so

3/x-5/x=2/x

4-x=3

if wondering why 4x-x = 3 because x basicly means 1 so then you answer will be

2/x-3

am not really sure if you wanted simplifyed but it might be this

The percent of rural neighborhoods in the county is 37.5%.

What is Ratio to Percentage Conversion?

It is given that the ratio of urban to rural neighborhoods in a county is 5 : 3.

[tex]\implies \frac{\text Urban}{Rural} =\frac{5}{3}[/tex]      -----(1)

The total neighborhoods can be given as,'

5 + 3 = 8 neighborhoods.

Thus, 5/8 parts are urban neigborhoods and 3/8 parts are rural neighborhoods.

Converting the ratio of rural neighborhoods to percentage, we get

[tex]\frac{3}{8} \times 100 =37.5 \%[/tex]

Therefore, the percent of rural neighborhoods in the county is 37.5%.

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The total number of practise booklets by 5 rather than 6 (the correct total number of schools).

The complete question is

The pie chart below shows the distribution of exercise books to six schools A, B, C, D, E and F in a town. School D was given 8,000 exercise books. F A B 60° 500 70% E 42° 80° D C​

(i) How many exercise books were given to each

of the rest of the schools?

(ii) What is the average number of exercise books given to the schools?

(iii) How many schools had less than the average number of exercise

books?

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The mean will increase because the new score of 100 is higher than the previous score of 95.

This dataset is from an exam and has several different statistics, such as the number of students, the mean, standard deviation, median, maximum score, range, and mode.

After a grading mistake was corrected, the student who originally got a 95 now has a 100. This will affect the mean, median, maximum score, and range of the dataset.

The maximum score will change from 95 to 100. The range will also increase, as the difference between the minimum and maximum scores will be larger.

The standard deviation may or may not change, as it depends on the distribution of the scores in the dataset.

If the new score of 100 is significantly different from the other scores, it could increase the standard deviation.

In conclusion, correcting a grading mistake can greatly affect the statistics of a dataset and it is important to understand the impact it may have on the results.

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Answer:

345 free throws

Step-by-step explanation:

To find the total number of free throws Caroline attempted, we can set up the equation: (total free throws) x 0.20 = 69 (missed free throws)

Solving for the total free throws:

(total free throws) = 69 / 0.20

(total free throws) = 345

So Caroline attempted 345 free throws in the season.

The image occupy 1250 inches².

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

The aspect ratio of screen 4:3 and the screen is 2500 square inches.

so, the width of the screen is = 2500/ 4.3 = 581.40 inches

As, the image displayed has an aspect ratio of 16:9.

The Area of image is

= 581.40 x 9/16

= 1250 inches².

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The first Epistle of John was written about AD of between 95 and 110 . So, by this our option should be 97 AD, which is true.

The Fourth of the Catholic Epistles, The First Epistle of John[a] is the first of the Johannine epistles in the New Testament. The authorship of the Johannine writings is disputed among academics. The First Epistle's author is identified as John the Evangelist, who most scholars do not consider to be the same person as John the Apostle. The three Johannine epistles are thought to have been written by the same person by the majority of scholars, however it is unclear if the same person wrote the Gospel of John.

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Total time taken to fill the 960 cubic feet pool is  1440 minutes. = 24 hrs = 1 day.

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid may become a cube by varying the lengths of the edges or the angles between the faces.

Features of a Cuboid :

A cube is a specific instance of a cuboid in which the length, width, and height are all equal. Accordingly, a cuboid is a cube.

The total volume of the cubic pool

with length = 20 feet

breadth = 12 feet

Depth = 4 ft

Volume (V) = 20 * 12*4 = 960 cubic feet.

1 cubic foot of volume = 7.5 gallon of water.

Total water required to fill the tank = 7.5 * 960 = 7200 gallon

The pool is filled at a 5 gallons of water per minutes so the

total time taken to fill the 960 cubic feet pool is = 7200/5 = 1440 minutes. = 24 hrs = 1 day.

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Total number of boys = 9

Total number of girls = 6

Let the no. of girls nick has be x

no. of boys nick has = x + 4

no. of boys pete has = x (given)

no. of girls pete has = y

No. of boys john has = z

no. of girls john has = c

we know that, x + x + 4 + z = 9,    

2x + z = 5

Let's now take a look at the possible values of x and z.

If x = 0, z = 5

If x = 1, z = 3

If x = 2, z = 1

(These are the possible number of boys nick and pete have.)

If pete has 0 boys, nick has 4 boys.

If pete has 1 boys, nick has 5 boys.

If pete has 2 boys, nick has 6 boys.

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There are 26 automobiles and 13 vans available for the field excursion.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. A mathematical statement that expresses the connection between two values is simply characterized as an equation. In an equation, the two values are usually equated by an equal sign. Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). A linear equation can include several variables.

Here,

If c represents the number of cars and v represents the number of vans,

5c+8v=234

c=2v

10v+8v=234

v=234/18

v=13 vans

c=26 cars

The number of cars for field trip is 26 and number of vans is 13.

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In the given trapezium/trapezoid ABCD, the value for the measure of ∠ADC is obtained as 157.4°.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

A trapezoid is also known as a trapezium.

A trapezium ABCD is given.

BE represents the height of the trapezium.

In Δ ABE use the trigonometric ratio since it is a right-angled triangle, to find the unknown ∠A.

cos θ = base / hypotenuse

Substitute the values in the equation -

cos θ = AE / AB

cos θ = 12 / 13

θ = 22.62°

The value of ∠A or ∠BAC is 22.62°.

Now ∠BAC and ∠ADC lie on the sample plane.

So according to the properties of a trapezium, the angles that lie on the plane have a sum of 180°.

The equation for the statement is -

∠BAC + ∠ADC = 180°

Substitute the values in the equation -

22.62° + ∠ADC = 180°

∠ADC = 180° - 22.62°

∠ADC = 157.38° ≈ 157.4°

Therefore, the measure of ∠ADC is 157.4°.

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the point of intersection of equation and the x value of that would be the solution. then You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1

Put both of those equations into slope intercept form (in order to be typed into the graphing calculator).

2x + 3y = 16.9

3y = -2x + 16.9

y = (-2/3)x + 16.9/3

5x = y + 7.4

5x - 7.4 = y

So in the graphing calculator,

Y1 = (-2/3)x + 16.9/3

Y2 = 5x - 7.4

Then find the point of intersection and the x value of that would be the solution.

You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1

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complete question is

Solve the system of linear equations by graphing.

2x + 3y = 16.9

5x = y + 7.4

What is the solution to the system of linear equations? Round to the nearest tenth as needed.

To show the work:

68 ÷ 0.4 = 170

Explanation:

You can think of dividing by a fraction as multiplying by its reciprocal. The reciprocal of 0.4 is 1/0.4.

So instead of dividing 68 by 0.4, you can multiply it by 1/0.4, which is the same as multiplying by 2.5.

68 * 2.5 = 170

Answer: 33/14

Step-by-step explanation:

Answer:

a:b:c = 20:15:8

Step-by-step explanation:

a:b=4:3 = 20:15

b:c=5:2= 20:8

so a:b:c = 20:15:8