Ms. Langlois has 26 pencils and Mr. Cox has a certain number of pencils. Write an expression that represents the combined number of pencils Ms. Langlois and Mr. Cox have.

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. We can write the values of AB and BC as -AB = 6 units,AC = 8 units

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that -

{B} is between {A} and {C}. Also : AB = 2x, BC = 3x - 1, AC = 14.

We can write -

AC = AB + BC

14 = 2x + 3x - 1

5x = 15

x = 3

So -

AB = 2 x 3 = 6

AC = 3 x 3 - 1 = 8

Therefore, we can write the values of AB and BC as -

AB = 6 units

AC = 8 units

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For all values of x that satisfy |x| < 1/2, |cos(x) - (1 - x^2/2)| is less than or equal to a very small positive number.

The Taylor series for cos(x) is:

cos(x) = 1 - x²/2 + x⁴/4! - x^6/6! + ...

So, if |x| < 1/2, then:

|cos(x) - (1 - x²/2)| = |x²/2 - x⁴/4! + x⁶/6! + ...|

This expression on the right-hand side is a sum of absolute values of the terms in the Taylor series expansion of cos(x), which are all positive for |x| < 1/2. Therefore, the absolute value of the expression on the right-hand side is less than or equal to the sum of all of these positive terms, which approaches 0 as x approaches 0.

Therefore, for all values of x that satisfy |x| < 1/2, |cos(x) - (1 - x²/2)| is less than or equal to a very small positive number.

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Answer:

54 is the answer of pradnya age

There are 5 ways that the sum of the dice be equal to 6 if a pair of distinct dice are rolled one time

It is the ordered arrangement of members belonging to a set with no repeats.

Analyzing the possibilities for the sum of the dice be equal to 6, assuming that each die has six sides:

Red die = 6 sides

Blue die = 6 sides

The possibilists are:

(Bleu, red)

(1,5)

(2,4)

(3,3)

(4,2)

(5,1)

There are 5 ways to get at sum of 6 if a pair of distinct dice are rolled one time

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Correct option is B, the graph represents the inequality y ≤ - x + 9.

Both mathematical expressions that are created by joining two expressions are called inequalities. The equation's two expressions are deemed to be equal when the equals sign (=) is present. The characters >, or indicate that the two expressions are not necessarily equal in an inequality.

We may see the values that an inequality reflects by placing inequality on a number line. We create a straight line and identify the end points with either an open circle or a closed circle in order to represent inequalities on a number line.

For the given graph,

y ≤ - x + 9

Put x = 0

y ≤ 9

The above condition is correct for the given graph.

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The midline of the graph is a horizontal line with y = 8.5.

The midline of a sinusoidal graph is the average of its maximum and minimum values, which represents the average height of the graph over one period. To find the midline, we need to find the average of the y-values of the maximum and minimum points.

The maximum point is (4,12) and the minimum point is (11,5), so the average of the y-values is (12+5)/2 = 8.5. This represents the y-intercept of the midline, which is a horizontal line. Therefore, the midline of the graph is a horizontal line with y = 8.5.

The midline of a sinusoidal graph separates the graph into two parts: the portion above the midline, where the graph is increasing, and the portion below the midline, where the graph is decreasing. The midline also provides important information about the amplitude and frequency of the graph.

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Answer:

y = 1/4x + 8

Step-by-step explanation:

-x+4y=32

4y = x + 32

y = 1/4x + 8

The S&P 500 and XYZ Inc. have a positive linear relationship.

The covariance between two variables provides information about the relationship between them, but it does not clearly measure the strength or type of the relationship. A positive covariance means that the variables move in the same direction, while a negative covariance means that the variables move in opposite directions.

In this case, the covariance between the S&P 500 and XYZ Inc. is 6,317.50, which is a positive value. This suggests that there is a positive linear relationship between the two variables, meaning that as the S&P 500 increases, XYZ Inc. also tends to increase, and vice versa. However, to fully understand the relationship between the two variables, it is necessary to calculate other measures, such as the correlation coefficient, which provides a standardized measure of the power and direction of the relationship between two variables.

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Answer:

1.71 meters.

Step-by-step explanation:

To work out Jodie's height, we can use the formula for body mass index (BMI):

BMI = weight (kg) / height (m)^2

We know that Jodie's BMI is 19 and her weight is 55 kilograms. We can use this information to solve for her height.

Rearranging the formula to solve for height:

height = √(weight / BMI)

Substituting in Jodie's weight and BMI:

height = √(55 / 19)

height = √(2.89)

height = 1.71 meters

To 2 decimal places, Jodie's height is 1.71 meters.

With a Body Mass Index (BMI) of 19 and a weight of 55 kilograms, the height of Jodie is 1.70 meters.

We know,

BMI = Weight of a person in kilograms (w) .........(i)

    Square value of height in meters (h^2)

(w) = 55 Kg

BMI = 19.

Substituting the values in equation (i),

h^2 = 55/19,

or, h^2 = 2.89 meters,

or, h = √2.89 meters,

or, h = 1.70 meters.

Therefore, at a BMI of 19 and a weight of 55 Kilograms, Jodie has a height of 1.70 meters.

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what went wrong

the student did not cross multiply, and instead multiplied within each fraction.

rework the problem

mx24=8x15

m=120/24

m= 5

helpful strategy

draw a line from each value to the one you're multiplying it by

practice problems

12/z = 15/20

Pythagoras theorem states that in a right angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can represent the length of the hypotenuse as "c", and the lengths of the other two sides as "a" and "b". So the equation is:

c² = a² + b²

To form an equation in x we can use a and b as variable, so we can substitute a = x and b = x-3, the equation becomes:

c² = x² + (x-3)²

To solve for c we can expand the second square and get:

c² = x² + x² - 6x + 9

Now we can add x² on both sides and get:

x² + x² = 6x - 9 + c²

We can combine like terms and get:

2x² = 6x - 9 + c²

Now we can move all the terms to one side and get:

2x² - 6x + 9 - c² = 0

Now we have an equation of a quadratic form with variable x, which can be solved using the quadratic formula.

x² = (6/2)x - 9/2 = 3x - 9/2 = 3x - 4.5 = 0

It can also be factored to get the solutions x = 4.5, x = 0

So the solutions to this equation are x = 4.5, x = 0.

The toy cars Anna must sell for her revenue to equal her expense is 4 toy cars. The result is obtained by using the concept of calculating algebra.

To calculate the algebra with one variable, sum up all the same variable and count the value.

Anna want to sell toy car at a craft fair. Each car is sold at a price of $ 12. The material for each car cost $ 3.50 and the table rental at the fair is 34 dollar for the day.

Find the toy cars must Anna sell for her revenue to equal her expense!

We have

Let's say

Revenue = Expense

a × $12 = (a × $3.5) + $34

12a = 3.5a + 34

12a - 3.5a = 34

8.5a = 34

a = 4 toy cars

Hence, Anna must sell 4 toy cars so that her revenue is equal to expense.

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The probability of filling an order between day 3 and 5 is 0.67, or 67%.

The time it takes a wholesaler to fill an order follows a uniform distribution from three to six days. To find the probability that they will fill an order between day 3 and 5, we need to calculate the cumulative probability of the uniform distribution between these two values.

The cumulative probability of a uniform distribution between two values a and b is given by:

P(a <= X <= b) = (b - a) / (max - min)

Where X is a random variable representing the time it takes to fill an order, min is the minimum value of the distribution (3 days), and max is the maximum value of the distribution (6 days).

So, for the uniform distribution between 3 and 5 days, the cumulative probability is:

P(3 <= X <= 5) = (5 - 3) / (6 - 3) = 2 / 3 = 0.67

This means that the probability of filling an order between day 3 and 5 is 0.67, or 67%. In other words, the wholesaler has a 67% chance of filling an order between day 3 and 5.

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Let x be the number of child tickets sold on Wednesday. Then, the number of adult tickets sold can be represented as 156 - x.

The total amount of money generated from the sale of child tickets is 5.80x, and the total amount of money generated from the sale of adult tickets is 9.70(156 - x). The total sales for the day were $1290.90, so we can set up the following equation:

5.80x + 9.70(156 - x) = 1290.90

Expanding the right-hand side and solving for x, we can isolate x:

5.80x + 1481.20 - 9.70x = 1290.90

-4.90x + 1481.20 = 1290.90

-4.90x = -190.30

x = 39

So, 39 child tickets were sold on Wednesday.  This is because the total number of tickets sold is 156, and since we know the number of child tickets sold, we can calculate the number of adult tickets sold by subtracting the number of child tickets from the total.

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The inequality for the range of the possible length for the third side is  100<x<500.

Inequalities can be defined as expressions that involve the use of symbols such as >, <, ≥, and ≤. In order to solve an inequality, we need to find what is called its range, or ranges, which are values that can satisfy the given inequality.

We already know that no side of a triangle can exceed the sum of the other two sides. The third side needs to be less than 500 (300 + 200) and greater than 100 ( 300 - 200)

So, our inequality is ⇒ 100<x<500.

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The measurement of the angle OP is 39

The given parameters that will help us to answer the question are

R is mid point of OQ

S is mid point of PQ

RS = 3x + 38

OP = 4x- 14

R is mid point of OQ and S is mid point of PQ;

By using mid point theorem

[1/2][OP] = RS

This implies that So,

[1/2][3x + 38] = [4x- 14]

[3x+38] = 2[4x- 14]

Opening the brackets we have

3x+38=8x-28

Collecting like terms

3x-8x=-28-38

-5x=-66

Making x the subject of the relation we have

x = -66 / -5

x = 13.2

Therefore RS = 3(13.2) + 38 = -11.4

OP = 4(13.2)- 14=38.8

Measurement of OP = 39 approximately

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The radius of each sphere is 0.63 cm.

What is Sphere?

It is given that 15 solid spheres are made by melting a solid metallic cone.

The base diameter (D) of  solid metallic cone is 2 cm and its height (H) is 15 cm.

So, the radius (R) of the solid metallic cone is 1 cm.

Now, volume of the cone (V) can be given as,

[tex]V = \frac{1}{3} \pi R^{2} H\\\implies V = \frac{1}{3} \pi \times 1^{2} \times 15[/tex]

Let the radius of the solid sphere be r.

Then, the volume of one sphere (V') can be given as,

[tex]V'=\frac{4}{3}\pi r^{3}[/tex]

The volume of 15 spheres can be given as,

[tex]V' \times 15=\frac{4}{3}\pi r^{3} \times 15[/tex]

Here, Volume of solid metallic cone = Volume of 15 solid spheres

[tex]\implies V = 15 \times V'\\\implies \frac{1}{3} \pi \times 1^{2} \times 15 = 15 \times \frac{4}{3}\pi r^{3}[/tex]

Solving for r, we get

[tex]r^{3} =\frac{1}{4}\\ \implies r=\sqrt[3]{\frac{1}{4}} \\\implies r= 0.63[/tex]

Therefore, the radius of each sphere is 0.63 cm.

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True, x-1 is a factor of P(x) = 17x¹² + 8x⁵ – 25.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.

Given function

P(x) = 17x¹² + 8x⁵ – 25

P(1) = 0

By the Remainder Theorem,

Dividend = Divisor * Quotient + Remainder

P(x) = (x – 1). Q(x) + P(1)

P(1) = 0

P(x) = (x – 1). Q(x)

Hence, x-1 is a factor of P(x).

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The average rate of change for this function for the interval from x = 2 to x = 4 is 6.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is a relationship between a set of inputs and a set of allowable outputs that has the condition that each input is associated to precisely one output. Let A and B be any two non-empty sets; mapping from A to B is only a function if every element in set A has one end and only one image in set B.

Here,

The average rate of change for this function between x = 2 and x = 4 is 6.

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The constant of proportionality is 6.

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. It is also known as unit rate and it is usually expressed by k.

Mathematically, k = y/x.

To find the Constant of Proportionality, pick any point from the graph. That is:

Point (20, 120). Thus, x = 20, y = 120  

Constant of Proportionality (k) = y/x

k = 120/20 = 6

The graph is proportional because the Constant of Proportionality of nay point on the graph is the same.

What I see is that the graph starts from the origin. That is the initial value of x and y are zero.

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On solving the provided question, we can say that the linear equation is 7x + 4y = 25.25 => x - 28 = -25.25 and cost is $35.43

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

Let x and Y represent the unknowable costs of a single hot dog and soft drink, respectively. We require two equations in order to solve for the two unknowns.

Equation 1 says that it costs $35 to buy 10 hot dogs and 5 soft drinks, or 10x + 5y = 35.

Equation 2: A total of $7.25 is spent on 7 hot dogs and 4 soft beverages, or 7x + 4y = $7.25.

[tex]10x + 5y = 35\\5y = 35 - 10x \\y = 7 - 2x \\[/tex]

[tex]7x + 4y = 25.25\\7x + 4(7-2x) = 25.25\\7x + 28 - 8x = 25.25\\-x + 28 = 25.25\\x - 28 = -25.25[/tex]

cost is $35.43

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It is difficult to predict the exact value of the correlation coefficient between crime rate and educational attainment across metropolitan areas.

However, it is often observed that there is a negative correlation between these two variables, meaning that as the level of educational attainment increases, the crime rate decreases.

There is evidence to suggest that higher levels of education are associated with lower levels of criminal behavior and better job opportunities, which can help to reduce crime in a community.

On the other hand, there are many other factors that can affect crime rates, such as poverty, unemployment, and population density, so the relationship between crime and education is complex and multi-dimensional.

It is also possible that the correlation coefficient between crime rate and educational attainment could be close to zero or even positive in some cases, depending on the specific metropolitan area and the data available.

Therefore, it is not possible to definitively say that the correlation coefficient will be negative, positive, zero, or none of the above.

Further analysis and study would be needed to determine the specific relationship between crime rate and educational attainment in any given metropolitan area.

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The value of the expression is 10.4

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

38÷[(−2)4+|−27÷9|]−(−18).

From the innermost grouping, we have

38÷[(−2)4+3]−(−18).

Remove the inner bracket

38÷[-8+3]−(−18).

So, we have

38 ÷ [-5] + 18

Evaluate

10.4

Hence, the solution is 10.4

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The maximum mortgage payment allowed for someone with an annual salary of $56,750 is $1891666.

According to the 28/36 guidelines, 28% of your gross monthly income should be spent on housing finances, and 36% of your total monthly income can be considered debt-free income.

Allow Total gross monthly income to equal $ x

The debt amount is $ 56,750.

So, 36% of x = $ 56,750

36x/100 = 56,750

x = 56,750 x 100 / 36

x = 157638.8

Annual income = 12 x 157638.8

= 1891665.6

= $1891666

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Answer: To determine what fraction of the cake is left convert the cake to 8ths which is 8/8. Subtract;. 8/8–7/8=1/8. The fraction left is 1/8.

7 answers

·

4 votes:

Let’s identify all the quantities here. [math]\frac{5}{8}[/math] is what all the g

Step-by-step explanation:

Answer:36

Step-by-step explanation:

Answer:

Step-by-step explanation:

A proportional relationship between two variables, x and y, is such that there is a constant of proportionality, k, that exists between the two variable, such that, y = kx.

Constant of proportionality (k) = y/x.

9) The relationship is proportional because 18% of dinner bill is being donated to local schools

So 18% of 50 is 9

So out of $50 of dinner bill, $9 will go towards donation.

10) No, the relationship is not proportional.

The cost of mailing6-ounce letter cannot be determined

The missing value is -3 = 7- 10.

Integers come in three types:

Given:

We have -3 = 7 - x

As, we know from the integers when we perform addition and subtraction in integers the answer will get the sign of larger number.

Here -3 shows the larger number is negative number.

But here we have 7 as positive integer which shows x > 7.

So, -3 = 7- x

-3-7 = -x

-10 = -x

x= 10

thus, we can write -3 = 7-10

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(E) 7/6 π-√3/2

We divided the white region into 5/6 of a circle with radius $1$ and two equilateral triangles with side length $1$ by drawing four lines from the intersection of the semicircles to their centers. This gives the white region a size of 5/6 π+2. √3/4=5/6π+√3/2. The area of the shaded region is equal to the area of the white region minus the area of the large semicircle. This is equal to 2 π-(5/6 π+√3/2)=7/6 π-√3/2.

 

Note

First, it is 5/6 of a circle because the middle sector has a degree of 180-2.60=60, resulting in 60/360=1/6 of a circle.

The other two each have an area of 180-60/360=1/3 of a triangle

Therefore, the total fraction of the circle IS 1/6+2.1/3=1/6+4/6=5/6


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well, we know there are 60 minutes in 1 degree, so in 40 minutes that'll be 40/60 degrees or namely 2/3 of a degree.

We know that 180° is π radians, so let's find 43 ⅔ degrees

[tex]\stackrel{mixed}{43\frac{2}{3}}\implies \cfrac{43\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{131}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\\\ \frac{131}{3}&x \end{array}\implies \cfrac{180}{~~ \frac{ 131}{3 } ~~} = \cfrac{\pi }{x}\implies \cfrac{\frac{180}{1}}{~~ \frac{ 131}{3 } ~~} = \cfrac{\pi }{x} \implies \cfrac{180}{1}\cdot \cfrac{3}{131}=\cfrac{\pi }{x} \\\\\\ \cfrac{540}{131}=\cfrac{\pi }{x}\implies 540x=131\pi \implies x=\cfrac{131\pi }{540}\implies x\approx 0.762~radians[/tex]

The  solution to this system of equations −4x+9y = 9 and x−3y = − 6 is,

(10, 5)

By using the substitution method, the solution to this system of equations −3x + 3y = 4  and −x + y = 3 is, No solution

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

System of equation,

−4x + 9y =   9

 4x − 4×3y = − 4×6   (multiplying equation by 4)

 0  - 3y   = -15

         y  =  5

−4x + 9×5 = 5

-4x  = -40

  x  =  10  

Second, system of equations

By substitution method,

−3x + 3y = 4

 −x  +  y  =   3      

Both the lines are parallel ,

so they will never intersect each other

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