Find the measure of x.
14
X
48
x = [?]

320/31 gallons of hot water and 300/31 gallons of cold water are needed.

Here we are required to fill a 20-gallon bathtub and the water should be precisely 100° F.

It is given that hot water has a temperature of 175° F and cold water has a temperature of 20° F.

Let the amount of hot water used be x gallons.

Let the amount of cold water used be y gallons.

Since the bathtub has a capacity of 20 gallons,

x + y = 20                                                                                  [1]

or, y = 20 - x                                                                             [2]

The temperature after the water is mixed will be a weighted average of the temperature and amt of water used.

Hence we get,

(175x + 20y) / (x + y) = 100

from equation [1] we get

175x + 20y = 2000                                                                   [3]

from equations [2] and [3] we get

155x - 400 = 2000

or, x = 1600/155 = 320/31                                                        [4]

Similarly,

y = 20 - 320/31

= 300/31

Hence 320/31 gallons of hot water and 300/31 gallons of cold water are needed.

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Proportionately, the quantity of milligrams of vitamin c in 1 orange is 33.75 mg.

Proportion refers to the part of a whole contained in another value.

Proportion is a ratio representation, which is fractional in value.'

We depict proportions using decimals, fractions, or percentages.

The daily recommended allowance of vitamin c for a sixth grader = 45 mg

The content of 1 orange to the daily recommended allowance = 75%

75% of 45 mg = 33.75 mg.

Thus, 1 orange will proportionately contain 33.75 mg, which is 75% of 45 mg.

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Answer: A. To find the number of glass squares each student will receive, we need to divide the total number of squares by the number of students.

We can write this as:

x = number of glass squares per student

x = 1240 / 121

B. To find the number of squares each student will receive, we need to solve for x by dividing 1240 by 121.

1240 ÷ 121 = 10.246753246753247

C. Each student will get 10 whole glass squares.

D. The remainder in this context is the number of glass squares that cannot be distributed evenly among the students. In this case, the remainder is 30. It means that there will be 30 glass squares left over after each student has received 10 squares. It's like remainder in division where after dividing 1240 by 121 the quotient is 10 and the remainder is 30.

Step-by-step explanation:

Therefore, if the cafeteria sells all of the pancakes made for 75 people, they will make $525.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary method can be used to complete it.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

If the cafeteria sells all of the pancakes made for 75 people, and the original recipe makes 14 pancakes, they would need to make 1475 = 1050 pancakes.

If they charge $0.50 per pancake and they sell all 1050 pancakes, they would make 1050$0.50 = $525.

Therefore, if the cafeteria sells all of the pancakes made for 75 people, they will make $525.

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Therefore , the solution to the given problem of unitary method comes out to be he will have $870.

The unit method is a method of problem-solving that entails calculating the variable of one unit, multiplying that value, and then calculating the required value. To describe it simply, the unit method is employed to obtain a single entity value from a specified multiple. One pen costs 400 rupees, thus 40 needles would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Logic of matrices or operators, algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.

Here,

To address the issue,

if the person gets a gross biweekly salary of $840 and claims 2 extra withholding allowances,

their take-home pay would increase by $30.

thus,

They will have 840 + 30 = $870

Therefore , the solution to the given problem of unitary method comes out to be he will have $870.

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Answer: To divide two rational expressions, you need to first find the least common denominator (LCD) of the two expressions. The LCD is the least common multiple of the two denominators.

In this case, the rational expressions are x/(3x-1) and (x-2)/(2x). The LCD of these two expressions is (3x-1)(2x), which can be factored as 6x(x-1).

To divide the two rational expressions, you need to express each expression as a fraction with the LCD as the denominator.

The first expression, x/(3x-1), can be rewritten as (x * (2x))/(3x-1 * (2x)) = (2x^2)/(6x^2-2x).

The second expression, (x-2)/(2x), can be rewritten as ((x-2) * (3x-1))/(2x * (3x-1)) = (3x^2-3x+2)/(6x^2-2x).

To divide these two expressions, you can divide the numerators and the denominators separately:

(2x^2)/(6x^2-2x) ÷ (3x^2-3x+2)/(6x^2-2x)

= (2x^2) ÷ (3x^2-3x+2)

= (2/3)x^2 ÷ (x^2-x+2/3)

Therefore, the quotient of the rational expressions x/(3x-1) and (x-2)/(2x) is (2/3)

Step-by-step explanation:

With the help of equations we can say that, the wedding had 96 attendees.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

x is the total number of wedding attendees.

1/3 of the attendees =1/3 who chose pasta=1/3x----1

Those who selected chicken =5/12x---2

24 people opted for meat.----3

adding 1,2,3

x = 96

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The answer choice which represents a number line for the intersection of the given intervals is; (-∞, 2).

The answer choice which represents a number line for the union of the given intervals is; (-∞, ∞).

It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.

Since the given intervals are; (-∞, 2) and [0,∞).

It follows that the intersection of both intervals is the interval; (-∞, 2).

Also, the interval which represents the union of both intervals is; (-∞, ∞).

Hence, the image which represents both scenarios is attached.

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Only 3 & 5 from the set {1,2,3,4,5,6} are primitive root (mod7), therefore, sum of integers is 3 + 5 = 8.

A number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n in modular arithmetic. That is, g is a primitive root modulo n if for every integer a coprime to n, some integer k for which gk ≡ a (mod n).

The index or discrete logarithm of a to the base g modulo n is a value k like this. So, if and only if g is a generator of the multiplicative group of integers modulo n, g is a primitive root modulo n.

In Article 57 of his Disquisitiones Arithmeticae (1801), Gauss defined primitive roots and credited Euler with coining the term.

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The length of the leg of the right-angled triangle is (11√2) / 2. The correct option is C.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the right angles triangle has 45-45-90 angles. The hypotenuse is 11.

The length of the leg will be,

Cos45 = Base / Hypotenuse

1 / √2 = Base / 11

Base = 11 / √2

Rationalize the numbers,

Base = 11√2 / 2

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Answer: The value of p and q for which the system of equations represent coincident lines is p = 2 and q = 1.

Step-by-step explanation: To represent coincident lines, the two lines must be proportional. Therefore, the slope of the second line must be equal to the slope of the first line.

The slope of the first line is 3/2. The slope of the second line is p + 2q + 2/p + q + 1. Therefore, we set these two equal:

3/2 = p + 2q + 2/p + q + 1.

Cross multiplying, we get:

3(p + q + 1) = 2(p + 2q + 2).

Simplifying, we get:

3p + 3q + 3 = 2p + 4q + 4.

Combining like terms, we get:

p - q = 1.

Therefore, the value of p and q for which the system of equations represents coincident lines is p = 2 and q = 1.

Essentially, a contingency table with 10 rows and 11 columns has (D) 90 degrees of freedom.

A contingency table is a matrix-form table that shows how often different combinations of variables appear.

It's really popular in survey research, business intelligence, engineering, and scientific research. Basically, a contingency table with 10 rows and 11 columns has 90 degrees of freedom.

They are also sometimes known as two-way frequency tables and are used to show how often different combinations of variables occur.

A contingency table gives you an idea of how two variables relate to each other.

It displays one categorical variable along the rows and another categorical variable along the columns. It can help point out any interactions between them.

Therefore, essentially, a table with 10 rows and 11 columns has (D) 90 degrees of freedom.

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Complete question:

The degrees of freedom for a contingency table with 10 rows and 11 columns are:

A. 100

B. 110

C. 21

D. 90

The amount of GI is $35,468.

The amount of taxable income is $23,068.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Gross income = $35,468

Exemption = $12,400

Deduction = 0

Adjustment = 0

Taxable income.

= Gross income - Exemption

= 35,468 - 12,400

= $23068

Thus,

GI and taxable income are $35,468 and $23,068

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The percentage of people who are satisfied with the car are 60%.

In mathematics →

Given is that in a survey of 2000 people who owned a certain type of​ car, 1200 said they would buy that type of car again.

The percentage of people who are satisfied with the car are -

{x}% = (1200/2000) x 100

{x}% = (12/20) x 100

{x}% = 12 x 5

{x}% = 60

Therefore, the percentage of people who are satisfied with the car are 60%.

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A compound statement is a statement that combines two or more simpler statements using logical connectives such as "and", "or", "not", "if-then", "if and only if", etc. To write a compound statement in symbolic form, you can use logical symbols to represent the different parts of the statement.

"∧" (and) is used to connect two statements, meaning that both statements must be true for the compound statement to be true. For example, "P ∧ Q" is read as "P and Q" and represents the statement "P and Q are true."

"∨" (or) is used to connect two statements, meaning that at least one of the statements must be true for the compound statement to be true. For example, "P ∨ Q" is read as "P or Q" and represents the statement "P or Q is true."

"¬" (not) is used to negate a statement, meaning that the statement is false if the original statement is true and vice versa. For example, "¬P" is read as "not P" and represents the statement "P is false."

"→" (if-then) is used to connect two statements, meaning that if the first statement is true, then the second statement must also be true. For example, "P → Q" is read as "if P then Q" and represents the statement "if P is true, then Q is also true."

"↔" (if and only if) is used to connect two statements, meaning that the two statements are either both true or both false. For example, "P ↔ Q" is read as "P if and only if Q" and represents the statement "P is true if and only if Q is true."

For example, the compound statement "If it is raining, then I will bring an umbrella, but if it's not raining, I will wear sunglasses" can be written in symbolic form as:

(R → U) ∧ (¬R → S)

Where "R" represents the statement "it is raining", "U" represents the statement "I will bring an umbrella" and "S" represents the statement "I will wear sunglasses".

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The estimated perimeter of an ellipse if the major axis has a length of 15 ft and the minor axis has a length of 7.5 ft id found to be 37.3 feet .

Perimeter is calculated as

= 2*pi*r*r

=  2 *3.14 * sqrt (15/2² +7.5/2²)/2

= 6.28 x sqrt (56.25+14.0625/2 6.28) *sqrt (35.15625) 6.28 * 5.929270613

= 37.235 feat

An ellipse is the locus of all the points on a plane whose distances from two fixed points in the plane are always same. The fixed points, which are encompassed by the curve, are known as foci , singular of focus.

The constant ratio is the eccentricity of the ellipse and the fixed line is directrix. Eccentricity is an element of  ellipse which denotes elongation and is symbolized by the letter 'e'.

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The length of the fencing that the city needs to surround the park will be 380.50 yards.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards. Then the length of the rectangular park is calculated as,

8925 = L × 84

L = 106.25 years

Then the length of the fencing that the city needs to surround the park will be given as,

P = 2(106.25 + 84)

P = 2 × 190.25

P = 380.5 yards

The length of the fencing that the city needs to surround the park will be 380.50 yards.

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Answer:

The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

The system represents the cost of the beginner class will be $18 and the advanced class will be $24.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Both basic and expert magic lessons are available at Wacky Wizards. More than half as much is spent on the introductory class as there is on the advanced level. They made $390 last week by instructing 7 basic lessons and 11 advanced classes.

Let 'x' be the cost of beginner classes and 'y' be the cost of advanced classes. Then the equations are given as,

x = y / 2 + 6

y = 2x - 12             ...1

7x + 11y = 390      ...2

From equations 1 and 2, then we have

7x + 11(2x - 12) = 390

7x + 22x - 132 = 390

29x = 522

x = 18

Then the value of the variable 'y' is calculated as,

y = 2(18) - 12

y = 36 - 12

y = 24

The system represents the cost of the beginner class will be $18 and the advanced class will be $24.

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a. The current sale price for the computer system is given as follows: $618.4.

b. The amount paid by the club members, with the discount, is given as follows: $587.48.

The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.

The selling price is of:

$773.

The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:

0.8 x 773 = $618.4.

Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:

0.95 x 618.4 = $587.48.

The problem is given by the image presented at the end of the answer.

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If Elliot purchased 3 trick cameras and 4 fake snakes for $40 and  Kaci bought 7 trick cameras and 8 fake snakes for $85 , then the system of equations that can be used to find the cost of trick camera and fake snakes are [tex]3x+4y=40[/tex] and [tex]7x+8y=85[/tex] .

Elliot purchased 3 trick cameras and 4 fake snakes for $40  ;

Kaci purchased 7 trick cameras and 8 fake snakes for  $85 ;

let the number of trick cameras purchased be = x ;

let the number of fake snakes purchased be = y ;

So , the equation for Elliot's purchase is ⇒ [tex]3x+4y=40[/tex] ;

and the equation for Kaci's purchase is ⇒ [tex]7x+8y=85[/tex] ;

Therefore , the equations to solve for the number of trick cameras and number of fake cameras are  [tex]3x+4y=40[/tex] and [tex]7x+8y=85[/tex] .

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Answer:

Yes

Step-by-step explanation:

If there was 200 hundred dollars just subtract 50 dollars if there is still money then yes.

Answer: yes

Step-by-step explanation:

200-50=159

The process to show the vector field V(x,y,z) as conservative is show  below and the scalar potential f is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex]   .

A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .

The Gradient is vector that is made from partial derivatives of potential function .

The Vector function is given as , V(x,y,z) = [tex](yz^{2} )i + (xz^{2} )j + (2xyz)k[/tex] ,

So , we can write the partial derivatives function of potential function as :

[tex]\frac{\partial f}{\partial x} = yz^{2}[/tex] ; [tex]\frac{\partial f}{\partial y} = xz^{2}[/tex] ; [tex]\frac{\partial f}{\partial z} = 2xyz[/tex],

On Antidifferentiating any of the above three partial derivatives ,

we get ; [tex]f=xyz^{2} + C[/tex] , here the constant C can take any value ,

so , we take C as [tex]e^{\pi }[/tex] .

Therefore , the potential Function is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .

The given question is incomplete , the complete question is

Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .

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The approximate arc length rounded to the nearest hundredth, between each spoke is 54.9 mm.

Diameter = 559 mm, r = d/2 = 279.5 mm

Number of spokes = 32

π = 3.14

To solve this question, we have to use the formula of the length of an arc which is given as

L = θ/360 × 2πr

To calculate the angle between each spoke, let's divide 360 by 32

θ = 360/32

θ = 11.25°

Now we have the value of the angle, substitute it and solve for the length of the arc.

[tex]L_{arc}[/tex] = θ/360 × 2πr

= 11.25/360 × 2 × 3.14 × 279.5

= 54. 9 mm

Therefore the length of the arc is approximately 54.9 mm.

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Answer: x<-2 or -2>x<1 or x>1

(-infinity,-2) U (-2,1) U (1,infinity)

Step-by-step explanation:

on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]

value of x from the given equation comes out to be 13.5

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According to unitary method, cat takes 12 steps to cover 9 feet.

Measure your stride length or assume that it is 2.2 feet for women and 2.5 feet for men to determine it. Add the stride length to the number of steps, for example, 2.2 feet multiplied by 1,000 feet equals 2,200 feet. The answer is 2,200 ft / 5,280 0.42 mi when expressed in miles.

Given, it takes a dog three steps to cover the same distance as a cat four steps.

4 steps of a cat = 3 steps of a dog

12 cat steps equal (3/4)*12 to 9 dog steps.

Additionally, a dog's step covers one foot.

The dog moves nine feet in nine steps.

So a cat takes 12 steps to cover 9 feet.

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The function f(x - 5/3) is translated 5/3 units right and the function f(x) - 5/3 is translated 5/3 units down.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, A function f(x) is transformed to f(x - 5/3) this results in f(x) is translated 5/3 units to the right along the x-axis.

And, The transformation f(x) - 5/3 is translated 5/3 units down along the y-axis.

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