The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $75,000 10-year term policy for a 25-year-old male. Round your answer to the nearest cent. A 5-column table with 6 rows titled Term Insurance. Column 1 is labeled Age with entries 20, 21, 22, 23, 24, 25. Column 2 is labeled 5-year term male with entries 2 dollars and 43 cents, 2.49, 2.55, 2.62, 2.69, 2.77. Column 3 is labeled 5-year term female with entries 2.07, 2.15, 2.22, 2.30, 2.37, 2.45. Column 4 is labeled 10-year term male with entries 4.49, 4.57, 4.64, 4.70, 4.79, 4.85. Column 5 is labeled 10-year term female with entries 4.20, 4.36, 4.42, 4.47, 4.51. a. $363.75 c. $183.75 b. $207.75 d. $338.25

There are 15 spiders in the backyard. The correct option is D

Let's begin by resolving the issue using algebra. Let's use "s" for the quantity of spiders and "d" for the quantity of dogs in the backyard.

As a result of the difficulty, we know that there are 3 times as many animals as there are spiders.

s + d = 3s

Simplifying this equation, we get:

d = 2s

We also know that there are 240 legs in the backyard, with each dog having 4  legs and each spider having 8. Thus, we can create the following equation:

8s + 4d = 240

Substituting d = 2s, we get:

8s + 4(2s) = 240

Simplifying and solving for s, we get:

16s = 240

s = 15

Therefore, there are 15 spiders in the backyard.

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The amount she charges for each necklace is $7.50 (option B).

Profit is the total difference between total revenue and total cost. Total cost is the sum of fixed cost and variable cost.

Profit = total revenue - total cost

Profit = (price x quantity sold) - (fixed cost + total variable cost)

Profit = (price x quantity sold) - (fixed cost +(variable cost per unit x quantity sold)

P = 7.5n - (2.25n + 15)

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Answer:

The Probability that a marble selected at random from the bag will NOT be green is 1/3

Step-by-step explanation:

The probability of selecting a green bag

                                            = Total No.of green bags/ Total number of bags

                                           =8/12

                                          = 2/3

Then the probability not of selecting a green bag  

                                                = 1 - The probability of selecting a green bag

                                                 = 1-(2/3)

                                                = 1/3

Answer:

To solve this problem, we can use the concept of direct variation, which states that two quantities vary directly with each other if they can be expressed as y = kx, where y is the dependent variable, x is the independent variable, and k is a constant of variation.

In this case, the distance traveled is the dependent variable and the speed is the independent variable. We are given that the distance traveled is 17.5 miles when the time (or speed) is 15 minutes.

So, we can set up the proportion:

distance / time = constant

17.5 miles / 15 minutes = k

Solving for k, we get:

k = 17.5 / 15

k = 1.16667 (rounded to 5 decimal places)

Now that we have the constant of variation k, we can use it to find the distance traveled in 2 hours (which is equivalent to 2 hours * 60 minutes/hour = 120 minutes).

distance = k * time

distance = 1.16667 * 120

distance = 139.99964 miles (rounded to 5 decimal places)

So, the correct answer is C) 140 miles, as it is the closest rounded value to the calculated distance of 139.99964 miles.

The expressions that are equivalent to 6x²y + 2xy⁵; are 2(3x²y + xy⁵), 2xy(3x + y⁴), xy(6x + 2y⁴) and 4xy(3/2x + 1/2y⁴). So, the correct options are a, b, e and g.

Algebra is known to be a branch of mathematics in which problems are represented as mathematical expressions using letters or variables (x, y, z, etc.) to represent unknown values ​​that may change. The purpose of algebra is to understand what the unknown values ​​are in order to find solutions to problems. The degree of an algebraic equation is the largest power that exists for the variables in the equation. Algebraic equations can be classified by degree as follows:

Equation A: 2(3x²y + xy⁵) = 6x²y + 2xy⁵

Equation B: 2xy(3x + y⁴) = 6x²y + 2xy⁵

Equation C: 2x²y(6 + 5y) = 12x²y + 10x²y²

Equation D: 6x²y.2xy⁵

Equation E: xy(6x + 2y⁴) = 6x²y + 2xy⁵

Equation F: 2y(3x + xy⁴)⁰ = 2y

Equation G: 4xy(3/2x + 1/2y⁴) = 6xy + 2xy⁵

Hence, Equation A, B, E and G are the equations found equivalent to the given equation, 6x²y + 2xy⁵.

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If the job takes Reba 1 hours, the cost would be $ 19 with either artist

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let's assume the number of hours that Reba takes to paint the window is h. Then, the total cost of the job with Reba would be:

Total cost with Reba = $19 ( h )  + $41

The total cost with Pete is already given as a flat rate of $60.

We want to find the number of hours that Reba would have to take to charge the same amount as Pete, so we can set the two expressions for the total cost equal to each other and solve for "h":

$ 19 ( h ) + $ 41 = $ 60

Subtracting $41 from both sides, we get:

$ 19 ( h ) = $ 19

Dividing both sides by $ 19, we get:

h = 1

So Reba would have to take 1 hour to charge the same amount as Pete.

To calculate the cost of the job with either artist if it takes Reba 1 hour, we can substitute h=1 into the expression for the total cost with Reba:

Total cost with Reba = $ 19 ( 1 ) + $ 41 = $ 60

Hence , this is the same as the flat rate quoted by Pete, so the cost of the job would be $60 with either artist if it takes Reba 1 hour

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Answer:

Step-by-step explanation:

Answer:

y = -3x + 1

Step-by-step explanation:

We are given a couple ordered pairs from this table. Lets use the slope formula so we can find the slope of this line:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Y2, y1, x2, and x1 are constants (points on the line). To make it easy, lets take the coordinates (0,1) and (1,-2). Then we just plug these points in and evaluate.

[tex]\frac{-2-1}{1-0}[/tex]

Evaluate both sides of the fraction.

[tex]\frac{-3}{1} =-3[/tex]

Now that we have the slope, we are given the y intercept coordinate, (0,1) which means the y-intercept is 1. To write it in y = mx + b form, we just plug in our numbers and were good to go.

[tex]y=-3x+1[/tex]

The solution set of f(x) > 0 is x ∈ (-2, 8).

To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.

Let's start by finding the domain of the function:

x² - 6x - 16 ≠ 0

We can solve for x by using the quadratic formula:

x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13

So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).

Now let's factor the numerator and denominator of f(x):

f(x) = (x + 10)/[(x - 8)(x + 2)]

The critical points occur where the numerator or denominator of f(x) changes sign.

The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.

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Answer:

  7²

Step-by-step explanation:

You want to know what 7×7 is when it is written using an exponent.

At its most basic, an exponent signifies repeated multiplication. It represents the number of times a value appears as a factor in the product.

The expression 7×7 has 7 as a factor 2 times. It can be written as 7 with an exponent of 2.

  7×7 = 7²

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The total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.

What is surface area?

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. A three-dimensional shape with height, breadth, and depth is referred to as having three dimensions, and surface area is a measurement of the total area that the surface of that shape occupies. In other terms, the surface area is the sum of the areas of all an object's sides.

Here, we have

Given:

Radius of cylinder = 8 units

Height of cylinder = 5 units

Thus:

Total Surface Area of a cylinder = 2 × 3.14 × 8 (8 + 5)

Total Surface Area of a cylinder = 50.24(13) = 653.12 sq. units.

Hence, the total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.

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The values are given below:

In mathematics, a function is a rule that assigns to each input value (or argument) from a set called the domain, a unique output value from a set called the range.

The term "maths function" is typically used to describe a specific type of function that is studied in mathematics, which can be represented using algebraic or other mathematical expressions.

Functions can be used to describe various phenomena in mathematics, science, and other fields, and they play a fundamental role in many areas of mathematics, including calculus, linear algebra, and number theory.

Some common examples of mathematical functions include polynomial functions, trigonometric functions, exponential functions, and logarithmic functions.

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Answer:

a) x < 0 excluding zero.

b) y ≥ 0

Step-by-step explanation:

a)

"x is negative": This means that x is less than zero. Negative numbers are any numbers less than zero, so this statement implies that x is a negative number. For example, x could be -1, -2, -3, and so on.

so answer is x < 0 excluding zero.

The inequality that expresses the statement "x is less than 0" using the expression "5a^2" would be:

5a^2 > 0 and x < 0

Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a". The inequality "x < 0" means that "x" is negative, or less than zero.

So, combining the two expressions, we get the inequality:

5a^2 > 0 and x < 0

b)

The statement "y is nonnegative" means that y is greater than or equal to zero. Therefore, the valid options for y are:

Therefore, the valid option for y is y ≥ 0.

As the given statement "y is nonnegative" cannot be expressed as an inequality involving the expression "5a^2". The expression "5a^2" is a polynomial in the variable "a", and it is not related to the variable "y" in the statement.

The inequality that expresses the statements "x is less than 0" and "y is non-negative" using the expression "5a^2" would be:

5a^2 > 0 and y ≥ 0 and x < 0

Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a".

The inequality "y ≥ 0" means that "y" is non-negative, or greater than or equal to zero.

The inequality "x < 0" means that "x" is negative, or less than zero.

So, combining the three expressions, we get the inequality:

5a^2 > 0 and y ≥ 0 and x < 0

I hope this helps!

The missing values of function rule, Y for corresponding value of X= (-4 ) and (-2) will be 9 and 3 respectively.

                                              [tex]X|-4 |- 2|\\ Y|\quad9\; | \quad3\;|[/tex]

Now for the given fucntion ,

By substituting the values of x into the equation [tex]y = -3x - 3[/tex] and solving for y, we can determine the values of y for [tex]x = -4\; and -2[/tex].

[tex]For \;x = -4:\\y = -3(-4) - 3\\y = 12 - 3\\y = 9[/tex]

Hence, for x =(-4), y= 9

[tex]For\; x = -2:\\y = -3(-2) - 3\\y = 6 - 3\\y = 3[/tex]

Hence, for x =( -2), y = 3

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Correct Question:Fill in the table using this function rule. y = - 3x-3

[tex]X|-4 |- 2|\\ Y|\quad?\; | \quad?\;|[/tex]

The value of x in the expression is y + 3

The expression given is written as

3x + 3= 3y + 6

collect the like terms

3x - 3y= 6-3

3x - 3y= 3

3x= 3 + 3y

x= 3 + 3y/3

x= 3 + y

x= y + 3

Hence the value of x in the expression is y + 3

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Answer:

13

Step-by-step explanation:

By counting the amount of dots there is on the graph you would end up with 13 trees.

A diagram that represents the expression |-5| include the following: A. graph A.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the absolute value of -5 or |-5|, an inequality that matches this graph is represented by the first diagram.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Hence, a person on a 2000 calorie diet  should eat more calories approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

A calorie is a measurement,  just like a teaspoon or an inch.  Calories are the amount of energy released when your body breaks down (digests and absorbs) food.  The more calories a food has, the more energy it can provide to your body

The  number of calories a person  should consume from vegetables versus carbohydrates depends on various factors  such as age, gender, activity level, body composition, and overall health status. However, in general, it is recommended that a person on a  2000 calorie diet should  consume more calories from vegetables than from carbohydrates.

The United States Department of Agriculture (USDA) recommends  that adults consume 2.5 to 3 cups of vegetables per day, depending on their age, gender, and level  of physical activity. On a 2000 calorie diet, this would amount to approximately 200-300  calories from vegetables.

For carbohydrates, the recommended  intake varies depending on the individual's energy needs,  but it generally accounts for 45-65% of their total calorie intake. This  equates to 900-1300 calories from carbohydrates on a 2000 calorie diet.

Therefore, a person on a 2000 calorie diet  should eat more calories  from vegetables than from carbohydrates, with an approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

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Generally, coordinates are a way of specifying the position of something in space, usually using a system of latitude and longitude or x, y, and z axes.

The coordinates of a physical location that serves as a hub for information, such as a data center or a library, then the answer will depend on the specific location you have in mind. To find the coordinates of such a place, you would need to use a mapping tool or geographic information system (GIS) to locate the facility and determine its latitude and longitude.

On the other hand, if you're asking about the "coordinates" of information in a more abstract sense, then this could refer to the ways in which information is organized or classified.

For example, a database might use a system of fields and tables to arrange information in a structured way, while a search engine might use algorithms to determine the relevance and ranking of different pieces of information based on factors like keywords, backlinks, and user behavior.

In conclusion, the coordinates of an information center is dependent on its nature in terms of its structural formation and the set goals to be accomplished by determining such coordinates.

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The ratio of whites to blacks is 20 to 3 ( or 20/3) in United States in 1990.

From a survey of the population of the United States, a circle graph (or, pie chart) was created on the information,

Population of the United States in 1990 :

White consists of 80%

American Indian, Eskimo, and Aleut consists of 1%

Black consists of 12%

Asian and Pacific Islander consists of 3%

Other Races consists of 4%

Let say the total population of the United States in 1990 was x.

By applying the formula of percentage to numbers we get,

The number of people who were white in 1990 in United States = 80% of x

= [tex][\frac{80}{100} ]x[/tex] = [tex]\frac{4}{5} x[/tex]

The number of people who were black in 1990 in United States = 12% of x

= [tex][\frac{12}{100} ]x[/tex] = [tex]\frac{3}{25} x[/tex]

Thus, we can calculate ratio as,

Ratio of whites to blacks = [tex]\frac{\frac{4}{5} x}{\frac{3}{25} x}[/tex] = 20/3

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We discard the negative solution, so EF = 8.725. Now we can substitute this value into the

How to solve the question?

To solve this problem, we can use the fact that if two triangles are similar, their corresponding sides are proportional.

We are given that triangle ABC is similar to triangle DEF. Therefore, we can set up the following proportion:

AB/DE = BC/EF = AC/DF

We are given the lengths of AB, AC, and BC, so we can substitute those values into the proportion:

11/DE = 7.9/EF = 7.6/DF

We are asked to find the length of DF, so we can isolate DF by cross-multiplying:

11EF = 7.9DE

7.6EF = 11DF

Now we can set the two expressions for EF equal to each other and solve for DF:

11EF = 7.9DE

11EF/7.9 = DE

1.39EF = DE

7.6EF = 11DF

DF = 7.6EF/11

Substitute the value of DE into the expression for EF:

DF = 7.6(1.39EF)/11

DF = 1.52EF

Now we need to find the value of EF. We can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle E:

angle E = 180 - angle D - angle F

We are not given the measures of angle D or angle F, so we cannot find angle E directly. However, we do know that triangles ABC and DEF are similar, so their corresponding angles are congruent. Therefore, we can use the measures of angles A, B, and C to find the measure of angle D:

angle D = angle A

angle D = 180 - angle B - angle C

Substitute the given values for angles A, B, and C:

angle D = 56.1 degrees

angle D = 116.9 degrees

We can use the Law of Cosines to find the length of EF:

EF²= DE² + DF²- 2(DE)(DF)cos(D)

EF²= 2.2² + (1.52EF)² - 2(2.2)(1.52EF)cos(D)

Substitute the two possible values for angle D:

EF²= 2.2²+ (1.52EF)² - 2(2.2)(1.52EF)cos(56.1)

EF²= 2.2²+ (1.52EF)² - 2(2.2)(1.52EF)cos(116.9)

Simplify both expressions:

EF²= 3.2596 + 2.3104EF²- 5.7024EF

EF²= 3.2596 + 2.3104EF² + 5.7024EF

Solve for EF using either equation:

-0.3104EF² + 5.7024EF - 3.2596 = 0

-0.3104EF² - 5.7024EF + 3.2596 = 0

Solve for EF using the quadratic formula:

EF = (-b ± √(b² - 4ac))/(2a)

EF = (-5.7024 ± √(5.7024² - 4(-0.3104)(-3.2596)))/(2(-0.3104))

EF = 8.725 or EF = -4.185

We discard the negative solution, so EF = 8.725. Now we can substitute this value into the

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Answer:

a. df = 1.52

Step-by-step explanation:

11 / 5 = 2.2

so... you divide the other number by 5

7.6 / 5 = 1.52

making the length of df, 1.52

hope this helps!!! :))))

Answer:

B. 314 m²

Step-by-step explanation:

Area of circle = π · r²

r = 10 m

π = 3.14

Let's solve

3.14 x 10² = 314 m²

So, the area of the circle is B. 314 m²

Answer:

Therefore, the original price of the dish was $12.61.

Step-by-step explanation:

Let the original price of the dish be "x".

After raising the price by 15%, the new price becomes:

x + 0.15x = 1.15x

We know that the new price is $14.50, so we can set up the equation:

1.15x = 14.5

To solve for x, we can divide both sides by 1.15:

x = 14.5 / 1.15

x = 12.61 (rounded to two decimal places)

The answer for given polynomial is 4,1,-1.

A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

The zeros of a function are the values of its variables that meet the equation and result in the function's value being equal to 0. The zeros of a function can be represented graphically as the x-coordinates (or x-intercepts) where the graph intersects the x-axis. The discriminant formula allows us to identify whether the zeros of a quadratic function are real, complex, or repeating. As a result, when a function f(x) = 0, its zeros are x values. Therefore, if f(a) = 0, then 'a' is a zero of f(x).

according to question,

(((([tex]x^{4}[/tex])-(3•(x³)))-5x²)+3x)+4  = 0

 (((([tex]x^{4}[/tex]) -  3x³) -  5x²) +  3x) +  4  = 0

Polynomial Long Division

Dividing :  x4-3x3-5x2+3x+4

                             ("Dividend")

By         :    x-4    ("Divisor")

dividend     x4  -  3x3  -  5x2  +  3x  +  4

- divisor  * x3     x4  -  4x3            

remainder         x3  -  5x2  +  3x  +  4

- divisor  * x2         x3  -  4x2        

remainder          -  x2  +  3x  +  4

- divisor  * -x1          -  x2  +  4x    

remainder              -  x  +  4

- divisor  * -x0              -  x  +  4

remainder                    0

Quotient :  x3+x2-x-1  Remainder:  0

the answer for the given polynomial by hit and trial method is 4,1,-1.

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The zeros of the polynomial is -1 , 1 and 4.

what is polynomial?

A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

Here the given polynomial is g(x) = [tex]x^4-3x^3-5x^2+3x+4[/tex]

To find zeros , take g(x) = 0 then

=> [tex]0=x^4-3x^3-5x^2+3x+4[/tex]

=> [tex]-x^4+3x^3+5x^2-3x-4=0\\[/tex]

=> [tex]-x^4+x^3+2x^3-2x^2+7x^2-7x+4x-4=0[/tex]

=> [tex]-x^3(x-1)+2x^2(x-1)+7x(x-1)+4(x-1)=0[/tex]

=> [tex]-(x-1)(x^3-2x^2-7x-4)=0[/tex]

=> [tex]-(x-1)(x^3+x^2-3x^2-3x-4x-4)=0[/tex]

=> [tex]-(x-1)(x^2(x+1)-3x(x+1)-4(x+1)=0[/tex]

=> [tex]-(x-1)(x+1)(x^2-3x-4)=0[/tex]

=> [tex]-(x-1)(x+1)(x^2+x-4x-4)=0[/tex]

=> -(x-1)(x+1)(x+1)(x-4)=0

=> x-1=0 , x+1=0 , x-4=0

=> x = -1,1,4

Hence the zeros of the polynomial is -1 , 1 and 4.

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The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.

(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:

Sampling error = z*(standard deviation/square root of sample size)

Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.

Substituting the values, we get:

Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%

Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.

(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:

Confidence interval = point estimate ± (z*standard error)

Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.

Substituting the values, we get:

Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)

Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.

(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:

New sample mean = 0.96 * 550 = 528

The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.

To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:

Confidence interval = sample mean ± (t*standard error)

Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.

The standard error can be calculated as follows:

Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31

Substituting the values, we get:

Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)

Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

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Answer:

x = 81.5°

Step-by-step explanation:

the secant- tangent angle x is half the difference of the measures of the intercepted arcs.

the sum of the arcs in a circle = 360°, then

unknown intercepted arc = 360° - (215 + 93)° = 360° - 308° = 52°

then

x = [tex]\frac{1}{2}[/tex] (215 - 52)° = [tex]\frac{1}{2}[/tex] × 163° = 81.5°

The given system of equations can be written as a vector equation [tex]7x^1+x^2-3x^3[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

An equation is a mathematical statement that expresses the equality of two expressions. It usually consists of two expressions separated by an equals sign (=). The expressions may contain numbers, variables, and operations, such as addition, subtraction, multiplication, and division. The solution of an equation is the value of the variable that makes the equation true.

Vector equation:

[tex](7x^1+x^2-3x^3)=7[/tex]

Part 2

Write the system as a matrix equation. Select the correct choice below and fill in any answer boxes to complete your choice.

Matrix equation:

=

A =

[7 1 -3

3 2 2]

B =

[7

0]

Conclusion:

The given system of equations can be written as a vector equation [tex](7x^1+x^2-3x^3)[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

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The area of the rhombus is 84 square units . Option C

The formula that is used for calculating the area of a rhombus is expressed with the equation;

A = a × h

Given that the parameters are;

From the information given, we have that;

If x = 12 units, y = 4 units, and h = 7 units.

Then the area of the rhombus will be;

Substitute the values into the equation

A = 12 × 7

Multiply the values

A = 84 square units.

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Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.

How to solve the question?

If Mrs. Jenkins gifts 10 cookies to her six sons, the number of cookies each son should get can be found by dividing the total number of cookies by the number of sons.

So, if we divide 10 cookies equally among six sons, we get:

10 / 6 = 1.6667

This means that each son should get approximately 1.67 cookies. However, since it is not possible to divide a cookie into fractions, the actual number of cookies each son would get may vary.

To distribute the cookies equally, Mrs. Jenkins can either give each son one cookie and then divide the remaining four cookies equally among the six sons. This would give each son one cookie and each son would get an additional 4/6 or 0.67 cookies.

Alternatively, Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.

In any case, the important thing is to ensure that each son receives an equal share of the cookies.

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YOUR COMPLETE QUESTION IS :-

Mrs. Jenkins gifts 10 cookies to her six sons if they share the cookies equally how many cookies should each son get