Literal Equations

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Using Venn diagram, The value of x is equal to 15.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that 50 students study at least one of the subjects geography (G), mathematics (M) and history (H).

Thus, 18 study only mathematics. 19 study two or three of these subjects.

23 study geography.

G + M - (x + 7) = 23 + 18 -(x + 7) = 19

23 + 18 -(x + 7) = 19

41 - x - 7 = 19

x = 15

Therefore,the value of x is 5.

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Answer: B

Step-by-step explanation:

For [tex]f(x)=3x-\frac{1}{2}[/tex], comparing it with slope-intercept form yields that the slope is [tex]3[/tex] and the [tex]y[/tex]-intercept is [tex]-1/2[/tex].

For the graphed function, the slope is [tex]\frac{-4-0}{-2-6}=\frac{1}{2}[/tex] and the [tex]y[/tex]-intercept is about [tex]-3[/tex].

Since the absolute value of the slope of the graphed function is less than that of [tex]f(x)[/tex], option B is correct.

If the volume of a cube decreases at a rate of 10 m/sec, then the  rate at which the side of the cube changes when the side of the cube is 2 m is -0.83 meter per second

The rate of  volume of the the cube decreasing = 10 meter per second

Consider the side of the cube is x

The volume of the cube = x^3

The rate of change of volume with respect to time

dV / dt = 3x^2 dx/dt

dV / dt = -10 meter per second

The dx / dt = (dV / dt) / 3x^2

We haver to find the rate at which side of the cube changes when the side of the cube is 2 meter

Then x = 2

dx / dt = -10 / (3 × 2^2)

= -10 / 12

= -0.83 meter per second

Therefore, the rate at which side of the cube changes when the side of the cubes is 2 meter is -0.83 meter per second

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We know that Lauren has 7/8 gallons of paint in total using simple mathematical operations.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.

The five basic operations in mathematics are addition, subtraction, multiplication, division, and modular forms.

So, we know that:
Lauren has 3/4 gallons of paint.

She later added 1/8 gallon of more paint.

The total paint she has is:

3/4 + 1/8

2(3) + 1/8

6+1/8

7/8

Therefore, we know that Lauren has 7/8 gallons of paint in total using simple mathematical operations.

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On solving the question, by help of Highest common Factor we got that He can only produce 4 bags before there are no more cookies left.

In mathematics, HCF is referred to by its full term, highest common factor. When dividing two or more numbers, the highest common factor (HCF) is two. For instance, the HCF of 4 and 6 is 2.

48 chocolate chips total.

64 vanilla cookies total.

100 raisin cookies are present.

[tex]HCF - 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24,48.\\64 = 1, 2, 4, 8, 16, 32 , 64\\100 = 1, 2, 4, 5, 10, 20, 25, 50, , 100.[/tex]

4 =  highest common factor of 48, 64 and 100

As a result, he can only produce 4 bags of cookies until none are left over.

For each bag:

cookies and chocolates = 48/4

= 12 each

64/4 vanilla cookies

= 16 each

100/4 raisins in cookies

= 25 each

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Answer:

a < -7

Step-by-step explanation:

Answer:

4.75

Step-by-step explanation:

The ratio of false positives to true positives is 3/49.

So, option B is correct.

A percentage is an expression that converts two ratios into an equal value. For instance, you may write the ratio as 1: 3 if there is 1 man and 3 women, meaning that 40% of the population is female and 14% is male. For any two numbers, the ratio formula is stated as a: b a/b. The percentage formula, on the other hand, is represented as a:b::c:da:b::c:da:b=cd. In mathematics, a ratio shows how many times one number is represented by another. For instance, if there are eight oranges and six lemons in a dish of fruit, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

The percentage of false positives=3%

The percentage of true positives=49%

Ratio=3/49

Therefore, the ratio of false positives to true positives is 3/49.

So, option B is correct.

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Answer: A linear equation in the form y = mx + b can be determined by examining the values in the table. To find the value of m, we can use the formula for the slope of a line, which is (y2 - y1) / (x2 - x1). Using the first and last values in the table, we can compute the slope as (7 - 15) / (4 - 0) = -1/4.

Therefore, the equation that represents the table is:

y = (-1/4) * x + b

We can use any of the given points to find the value of b. For example, using the point (1, 13), we can solve the equation to find b:

13 = (-1/4) * 1 + b

b = 14 - 1/4 = 13 3/4

Therefore, the final equation that represents the table is:

y = (-1/4) * x + 13 3/4

Answer

$7

Explaination :

3 bracelet - $5( for 1)

3 necklace - (unknown)

Total amount paid - $40

change - $4

Calculation for all 3 bracelet

$5×3=$15

Calculation for the real amount

$40-$4=$36

Calculation for 3 necklace

$36-$15=$21

Calculation for 1 necklace

$21÷3=$7

There reason I divide it with 3 was because I got the total amount for 3necklace now I only want 1..

Final answer - $7#

Hope this helped :)

Answer:

----------------------------

Each bracelet cost $5 and necklace costs x.

The total for 3 of each is:

Set equation and solve for x:

Answer:

The percent decrease is 70%.

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

The area of the image is, 7396 square pixels.

what is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Let x represent the length and the width of the image.

The area of the image and the border is represented by the expression

(x + 4)^2.  

Total area - area of image = Area of border

(x + 4)^2   -          x^2          =     704

⇒ x^2 + 8x + 16 - x^2 - 704 = 0

                             8x - 688 = 0

                                       8x = 688

                                         x = 86

The image will be 86 pixels by 86 pixels.

The area becomes  86*86 = 7396 square pixels.

Hence, the area of the image is, 7396 square pixels.

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The answer is No because one x-value corresponds to two different

y-values.

What is the function?

Each element of X is given exactly one element of Y by a function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Here the given function is,

           x     y

           3     4

           4     4

           5     2

           5     5

From the table we can see that there are 2 values of x having same

y - value.

Hence, the given table does not represents a function.

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For the 5.5% coupon corporate bond, the coupon payment would be $55 per year. For the 6.45% coupon treasury note, the coupon payment would be $64.50 per year.

Calculations using percentages show how much a given number contributes to the total. It is computed by dividing the number by the sum and multiplying by 100. It is denoted by the sign "%." For example, if a basket contains ten apples, three of which are red, the proportion of red apples in the basket is 30% (3/10 x 100). In a wide range of disciplines, including business, statistics, and education, percentage is often utilized. Calculating interest rates, taxes, and other financial activities in the finance industry annually frequently uses percentages. The frequency of events or the likelihood of a certain outcome are both measured using this method in statistics. Calculating grades and evaluating a student's overall performance are both done using this in education.

How to solve?

For the 5.5% coupon corporate bond, the coupon payment would be 5.5% of $1,000 = $55 per year.

For the 6.45% coupon treasury note, the coupon payment would be 6.45% of $1,000 = $64.50 per year.

For the corporate zero-coupon bond maturing in 10 years, there are no coupon payments. The bond will only make a payment of $1,000 at maturity.

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The correct answer to this Question based on Frequency Tables is B

What are frequency Tables?

These are a form of storing data that is easy to manipulate and use it for required purposes

This is an easy way to store and use data than other storing Methods

Solution:

As we can clearly see that 13 students who have completed the review sheet have passed the exam whereas 4 students who havent Completed the review sheet have also passed the exam according to given frequency table

Means we can say that reviw sheet must have some important problems that are similar to problems asked in exam hence chances are more that if a student solves and completed review sheet he will get passed in the exam acc to given frequency table Hence Option B is correct answer

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Check the picture below.

Answer: no, not in any way

Step-by-step explanation: it does not matter how many times you multiple 12, you will never end up getting 44.

The following expression represents a 2-scale factor vertical stretch, a transformation of 4 units left, and a transformation of 1 unit down:

g(x) = 2f(x + 4) - 1

A vertical stretch of scale factor K is expressed as follows for the general function f(x):

g(x) = Kf(x).

Horizontal translation:

A horizontal translation of N units for a general function f(x) is written as:

g(x) = f(x + N).

The shift is to the left if N is positive and the shift is to the right if N is negative.

Vertical translation:

A vertical translation of N units for a generic function f(x) is expressed as follows:

g(x) = f(x) + N.

When N is positive, there is an upward movement and N shifts downward if it is negative.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2f(x)

Then we translate it into 4 units left:

g(x) = 2f(x + 4)

Then we translate 1 unit down:

g(x) = 2f(x + 4) - 1

This is the equation for the transformation.

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Answer:

v=50

Step-by-step explanation:

since the angle next to x+50 if you add them the rule is they will equal 180 degrees and that the entire triangle equals 180 degrees then the 2 other angles will equal v+50

v+v=v+50

 -v.  -v

v=50

hopes this helps

The area of the sector of circle G is calculated as; 18.85 sq. units

The formula for the area of a sector is;

A = θ/360 * πr²

where;

A is area

r is radius

θ is central angle

We are given;

Radius of sector; r = 12 units

Central angle; θ = 15°

Thus;

A = 15/360 * π(12)²

A = 18.85 sq. units

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Answer:

B

Step-by-step explanation:

Answer:

See Picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

8 1 5

Answer:

Not enough context

Step-by-step explanation:

We need the bar graph/information for the amount child and adult tickets cost.

The required possible lengths of the parking lot is 300.

The  perimeter of a shape is characterized as the complete length of its limit. The border of a not entirely set in stone by adding the length of the relative multitude of sides and edges encasing the shape.

The area of a shape is the "space encased inside the border or the limit" of the given shape. We compute the region for various shapes utilizing math equations.

Perimeter = 520 feet, area = 12000 feet

We know that,

Perimeter = 2(L + B)

2(L + B) = 520

(L + B) = 260--------(1)

And

Area = L×B = 12000

From equation(1),we get

L(L - 260) = 12000

L^2 - 260L = 12000

L^2 - 260L - 12000 = 0

On solving above quadratic equation

L = 300 or L = -40

Thus, possible value of length is 300.

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By using the concept of reflection, it can be calculated that-

Value of x is 6 and value of y is -7

What is reflection?

Reflection is a mathematical transformation in which a mirror image of an object can be formed with respect to a line called the line of reflection.

The point is (-2, -4)

(-2, 4) is reflected across y-axis

New coordinate after reflection = (2, -4)

By the problem,

(x - 4, y + 3) = (2, -4)

x - 4 = 2

x = 2 + 4

x = 6

y + 3 = -4

y = -4 - 3

y = -7

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Answer:

40° and 110°

Step-by-step explanation:

the sum of the 4 angles in a quadrilateral = 360°

the ratio of 2 angles = 4 : 11 = 4x : 11x ( x is a multiplier )

sum the 4 angles, equate to 360 and solve for x

140 + 70 + 4x + 11x = 360

210 + 15x = 360 ( subtract 210 from both sides )

15x = 150 ( divide both sides by 15 )

x = 10

Then

4x = 4 × 10 = 40°

11x = 11 × 10 = 110°

the measure of the 2 angles is 40° and 110°

The difference between the two is only 0.01 %. The first size is a better purchase for Unit Price even though both might be rounded off to $0.3/oz.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

A shampoo's unit price is its cost per ounce. It is a straightforward division problem that may be solved with a simple calculator or pen and paper.

The first size weighs 14.2 ounces and costs $3.98.

This shampoo's unit price is ($3.98/14.2 oz) = $0.28/oz ( rounded off to nearest cent)

The second size weighs 33.9 ounces and costs $9.98.

The second shampoo's unit price is ($9.98/33.9 oz) = $0.29/oz (also rounded off to nearest cent)

Hence, There is just a 0.01% difference between the two. Even though both sizes may be rounded to $0.3/oz, the first size is the preferable choice in terms of unit price.

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Complete Question-

A certain shampoo is available in two sizes. A 13.5 ounce bottle costs $2.19, A 29.2 ounce bottle costs $5.37. Find the unit price for each size. then state which size is the better buy based on the unit price. Round your answers to the nearest cent.?