what is
8/9 x 21/28
(Multiplying and Dividing fractions and/or Mixed Numbers) ​

Answer:

0.8

Step-by-step explanation:

-8.1+8.9=0.8

so the answer is 0.8

Answer: Density = 0.23 tons per cubic meter.

Step-by-step explanation:

Formula : \(Density=\dfrac{Mass(in \ ton)}{Volume (in\ m^3)}\)

1 ton = 32000 ounces

⇒ 1 ounce = 0.00003125 ton

⇒  7 ounces = 7(0.00003125)=  0.00021875 ton

1 gallon = 0.00378541 cubic meter

2.5 gallons = 0.009475 cubic meter

Density= \(\dfrac{0.00021875}{0.009475}\text{ tons per cubic meter}\)

\(\dfrac{21875}{94750}\text{ tons per cubic meter}\approx0.23\text{ tons per cubic meter}\)

Hence, Density = 0.23 tons per cubic meter.

Answer:

0.02 tons per cubic meter

Step-by-step explanation:

Answer:

x < 4

Step-by-step explanation:

Step 1: Write inequality

5x < 20

Step 2: Solve for x

Here we see that any number less than 4 will work. So numbers like 3, 0, or even -12587235897 would work.

Answer:

A-3, B-4, C-1, D-2

Step-by-step explanation:

A:

B:

C:

D:

Answer:

72

Step-by-step explanation:

Just multiply all them

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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A check or quadrangle is defined by the intersection of pairs of diagonals of a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides are parallel and have the same length. The opposite angles of a parallelogram are equal. A parallelogram is a unique type of quadrilateral with specific characteristics.

A quadrangle or check is defined as the intersection of pairs of diagonals of a parallelogram. In other words, it is the area inside the parallelogram that is divided into four triangles, each of which shares a common vertex in the center of the parallelogram.

The diagonals of a parallelogram are the line segments that connect the opposite vertices of a parallelogram. When these diagonals intersect, they form four triangles, which are also known as the parallelogram's "sub-triangles." The point where the diagonals intersect is called the center of the parallelogram, and it divides each diagonal into two equal parts.

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The Non-real solutions for the equation \(x^{4} -x^{3}+10x^{2} -16x-96=0\) are (-4i, 4i).

Non-real solution:

An answer to a mathematical equation with the root of a negative number that cannot be determined using solely real numbers—i.e., numbers that can be described along a single axis—is referred to as a non-real solution.

If a quadratic has a negative discriminant, then the quadratic equation has a Non-real solution.

Given,

         \(x^{4} -x^{3}+10x^{2} -16x-96=0\)

On factorizing the above equation, we get

             \((x-3)(x-2)(x^{2} +16)=0\)

Applying Zero Product Property,

\(x^{2} +16 = 0\)      or     \(x-3=0\)     0r     \(x+2=0\)

Taking \(x^{2} +16 = 0\), we get

                \(x^{2} =-16\)

                x = ± \(\sqrt{-16}\)

                x = ± 4i              [∵ i = √-1]

Hence,

      The Non-real solutions for the equation \(x^{4} -x^{3}+10x^{2} -16x-96=0\) are (-4i, 4i).

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Answer:

C

Step-by-step explanation:

edge 2026

The absolute value function that could represent this situation is:

\(|D - 42.67| = 0.002\)

The absolute value function is defined by:

\(|x| = x, x \geq 0\)

\(|x| = -x, x < 0\)

The diameter should be of 42.67 mm with an allowance of 0.002 mm. Thus, the absolute value of the difference between the diameter and of 42.67 should be of 0.002, that is:

\(|D - 42.67| = 0.002\)

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Answer:

3n/10

Step-by-step explanation:

The required algebraic expression when the that  total cost is $142.05.

That is $125.80 for Watermelon that weighs 185 lbs and $16.25 for 5 lbs of tomatoes.

=>Total cost = 3.25t +.68w

Given: Tomatoes cost $3.25 per lb while watermelons cost $.68 per lb.

Let w = weights of the tomatoes and watermelons.

The algebraic expression would be:

3.25t +.68w = Total cost

For 5 pounds of tomatoes and 185 lb of watermelon:

68(185) + 3.25(5)

=$125.80 + $16.25

= $142.05

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

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Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise

Answer:

Step-by-step explanation:

\(f(x)=-x-11\\\\\frac{f(9)}{f(-6)}\\\\ f(9)= -9-11\\- 20\\\\f(-6) = -(-6)-11\\= 6-11 = -5\\\\\\\frac{f(9)}{f(-6)}\\ \\= \frac{-20}{-5}\\ \\= 4\)

Answer:

4

Step-by-step explanation:

This means that where ever you see x in the function; f(x)= -x-11, you replace it with 9 for the numerator and -6 for the Denominator

=-(9)-11/-(-6)-11

=-9-11÷6-11

=-20÷-5

=4

The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.

In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.

The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.

By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.

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The domain of the function shown in the graph is the one in option A:

6 ≤ k ≤ 11

The domain of a function y = f(x) is the set of the inputs of the function. To identify the domain in a graph, we need to look at the horizontal axis (also called the x-axis).

On the graph we can see that it starts at x = 6 with a closed dot, and it ends at x = 11 also with a closed dot.

That means that these values belong to the domain, so we can write the domain as follows:

Domain = 6 ≤ k ≤ 11

(notice that the variable in the horizontal axis is k).

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Answer:

The pen is $52.50 and the cost of the pencil is $2.50.

Step-by-step explanation:

What is the answer if a pen and a pencil cost 55 dollars and the pen cost 50 more dollars than the pencil​?

—

Step 1: Let Statements

Let a be the cost of the pen

Let b be the cost of the pencil

Step 2: Write Equations

a + b = 55

a = 50 + b

Step 3: Find POI

Using substitution to find the POI of both equations:

50 + b + b = 55

50 + 2b = 55

2b = 55 - 50

2b = 5

b = 5/2 or 2.5

Substitute b = 5/2 to solve for a

a = 50 + b

a = 50 + 2.5

a = 52.5

Therefore, a = 52.5 and b = 2.5

Step 4: Concluding Sentence

The cost of the pen is $52.50 and the cost of the pencil is $2.50.

In statistical analysis, a hypothesis refers to a tentative explanation or prediction that is based on limited evidence and is subject to further investigation and testing. It is a statement that can be either true or false, and is typically formulated in such a way that it can be tested using statistical methods.

The hypothesis is often used to guide the research process, to help identify potential patterns or relationships in the data, and to evaluate the significance of the results.

Overall, the hypothesis plays a critical role in statistical analysis, as it provides a framework for understanding and interpreting data, and helps to ensure that research findings are reliable and valid.

A hypothesis in the context of statistical analysis is a tentative explanation or prediction about the relationship between two or more variables, which is subject to testing and empirical evaluation using statistical methods.

It is a statement that can be either true or false, and it is usually formulated in terms of the expected direction and strength of the relationship between the variables of interest.

The hypothesis is typically derived from existing theory, prior research, or common sense, and it serves as a guide for the collection, analysis, and interpretation of data in a scientific study.

The process of testing a hypothesis involves setting up null and alternative hypotheses, selecting an appropriate statistical test, collecting and analyzing data, and drawing conclusions based on the results of the analysis.

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Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.

The products of a measurements of the segments of two chords are equal if they overlap in a circle.

For the given arc length  of circle:

Let the intersection of the both chords be 'O'.

m∠KOL = 180 - x  ...eq 1 (linear pair).

By the  intercept chord theorem:

m∠KOL = (arc JM + arcKL)

Put the value of eq 1.

180 - x = 1/2(30 + 2x - 30)

180 - x = 1/2 * 2x

180 = x + x

x = 180/2 = 90

Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.

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Answer:

Press down the brake firmly and smoothly. ...

Don't brake and swerve the car at the same time. ...

Avoid using your transmission for quick stops. ...

Focus on where you want to go, not what you want to avoid.

After considering the given data we conclude that the answer for the given sub question regarding combination are
a) the number of different groups of 10 employees that can be selected is 14,307,292
b) the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is 77
c) employees who take public transit is 66
d) employees who drive to work is 11
e) employees that do not include anyone who takes public transit is 184,756
f) employees that do not include anyone who drives to work is 352,716
g) employees that consist of at least one person who drives to work is 14,054,576
h) employees that consist of at least one person who drives to work is 14,054,576
i) employees that consist of 5 people who take public transit and 5 people who drive to work is 365,904
j) employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is 6,270,840

a) This is a combination problem, where the order of selection does not matter. The formula for the number of combinations of n objects taken r at a time is \(nCr = n! / (r! * (n-r)!)\), where n is the total number of objects and r is the number of objects being selected. In this case, there are 32 employees and we want to select 10 of them, so the number of different groups of 10 employees that can be selected is:
\(32C10 = 32! / (10! * (32-10)!) = 14,307,292\)

b) We can add the number of groups that consist only of employees who take public transit to the number of groups that consist only of employees who drive to work. To find the number of groups that consist only of employees who take public transit, we can choose 10 employees from the 12 who take public transit. Similarly, to find the number of groups that consist only of employees who drive to work, we can choose 10 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is:
\(12C10 + 11C10 = 66 + 11 = 77\)

c) We can choose 10 employees from the 12 who take public transit, so the number of possible groups of 10 employees that consist entirely of employees who take public transit is:
\(12C10 = 66\)

d) We can choose 10 employees from the 11 who drive to work, so the number of possible groups of 10 employees that consist entirely of employees who drive to work is:
\(11C10 = 11\)

e) We can choose 10 employees from the 20 who either drive to work or do neither, so the number of possible groups of 10 employees that do not include anyone who takes public transit is:
\((20C10) = 184,756\)
f) We can choose 10 employees from the 21 who either take public transit or do neither, so the number of possible groups of 10 employees that do not include anyone who drives to work is:
\((21C10) = 352,716\)

g) We can subtract the number of possible groups of 10 employees that do not include anyone who takes public transit from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who takes public transit is:
\(32C10 - 20C10 = 14,122,536\)

h) We can subtract the number of possible groups of 10 employees that do not include anyone who drives to work from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who drives to work is:
\(32C10 - 21C10 = 14,054,576\)

i) We can choose 5 employees from the 12 who take public transit and 5 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist of 5 people who take public transit and 5 people who drive to work is:
\(12C5 * 11C5 = 792 * 462 = 365,904\)

j) We can choose 4 employees from the 12 who take public transit, 3 employees from the 11 who drive to work, and 3 employees from the 9 who do neither. Therefore, the number of possible groups of 10 employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is:
\(12C4 * 11C3 * 9C3 = 495 * 165 * 84 = 6,270,840\)
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If your target number of calories to lose weight is 1,703 per day, but you are consuming 2,399 calories per day, then your target is to consume approximately 70% of the calories you are currently consuming.

To find the percentage of the target calories in relation to the current calories, we can divide the target calories by the current calories and multiply by 100. So, the calculation would be:

Percentage = (Target Calories / Current Calories) * 100

Substituting the values, we get:

Percentage = (1,703 / 2,399) * 100 ≈ 70%

Therefore, your target is to consume approximately 70% of the calories you are currently consuming in order to meet your weight loss goal.

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Answer:

The rate of change of the cost of the taxi ride is $2.00 per minute.

Step-by-step explanation:

The derivative of f(x) = \(10^{(ln x)\) is (ln 10 / x) × \(10^{(ln x)\), which corresponds to option D.

To find the derivative of the function f(x) = \(10^{(ln x)\), we can use logarithmic differentiation.

Let's start by taking the natural logarithm of both sides of the equation:

ln(f(x)) = ln(\(10^{(ln x)\))

Using the logarithmic property of exponents, we can bring the exponent down:

ln(f(x)) = (ln x) ln(10)

Next, we differentiate both sides with respect to x:

(d/dx) ln(f(x)) = (d/dx) [(ln x) ln(10)]

Applying the chain rule on the right side, we have:

(d/dx) ln(f(x)) = (ln 10) × (1/x) × x

Simplifying, we get:

(d/dx) ln(f(x)) = (ln 10) / x

Finally, we can find the derivative of f(x) by multiplying both sides by f(x) = \(10^{(ln x)\):

(d/dx) f(x) = (ln 10) / x × f(x)

Since f(x) = \(10^{(ln x)\), we substitute it back into the equation:

(d/dx) f(x) = (ln 10 / x) × \(10^{(ln x)\)

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The question is -

This question is designed to be answered without a calculator.

d/dx(10^{ln x}) =

A. (ln x) 10^{ln x-1}

B. (ln 10) 10^{ln x}

C. (1/x) 10^{ln x}

D. (ln 10/ x) 10^{ln x}

Answer:

(a) The equation is 3 × x = 5 × (x - 1.5)

(b) The price of each item Spongebob bought is $3.75

The price of each item Patrick bought is $2.25

(c) The total cost of the items bought by Spongebob = $11.25 = The total cost of the items of items bought by Patrick bought

(d) The prices of the 3 items that Spongebob bought are $3.75 each. The prices of the 5 items that Patrick bought are $2.25 each  

Step-by-step explanation:

The given parameters are;

The number of items Spongebob bought = 3 items

The price of each item Spongebob bought = The same = x

The number of items Patrick bought = 5 items

The price of each item Patrick bought = Equal price = x - 1.5

The amount of money Spongebob paid = The amount of money Patrick paid

(a) Therefore, the equation with representing the expressions are;

The total price Spongebob paid = (The number of items Spongebob bought) × (The price of each item Spongebob bought)

The total price Spongebob paid = 3 × x

The total price Patrick paid = (The number of items Patrick bought) × (The price of each item Patrick bought)

The total price Patrick paid = 5 × (x - 1.5)

The equation is 3 × x = 5 × (x - 1.5)

(b) From the following equation;

The amount of money Spongebob paid = The amount of money Patrick paid

We have;

3 × x = 5 × (x - 1.5)

3 × x = 5 × x - 7.5

7.5 =  5 × x - 3 × x = 2 × x

x = 7.5/2 = 3.75

x = $3.75

Therefore;

The price of each item Spongebob bought = x = $3.75

The price of each item Spongebob bought = $3.75

The price of each item Patrick bought = x - 1.5 = $3.75 - $1.5 = $2.25

The price of each item Patrick bought = $2.25

(c) We check the total cost of the items of items bought by Spongebob as follows;

The total amount of cost of the items bought by Spongebob = 3 × $3.75 = $11.25

The total cost of the items of items bought by Spongebob = $11.25

The total cost of the items of items bought by Patrick bought = 5 × $2.25 = $11.25

The total cost of the items of items bought by Patrick bought = 5 × $2.25 = $11.25

The total cost of the items of items bought by Patrick bought = $11.25

From which we have;

The total cost of the items bought by Spongebob = $11.25 = The total cost of the items of items bought by Patrick bought

(d) The prices of the 3 items that Spongebob bought are $3.75 each. The prices of the 5 items that Patrick bought are $2.25 each.

Answer:

Point D

Step-by-step explanation:

Point D is where lines starting from A, B, and C intersect.

The values of x for which f(x) = g(x) are x = -6 and x = -7.

To determine the value(s) of x for which f(x) = g(x), we need to set the two functions equal to each other and solve for x.

Setting f(x) = g(x), we have:

x² + 7x + 33 = -6x - 9

Rearranging the equation:

x² + 7x + 6x + 33 + 9 = 0

Combining like terms:

x² + 13x + 42 = 0

Now, we can factor the quadratic equation:

(x + 6)(x + 7) = 0

Setting each factor equal to zero:

x + 6 = 0  or  x + 7 = 0

Solving for x:

x = -6  or  x = -7

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The solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112

what is trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can use the trigonometric identity:

cos(a)cos(b)sin(a)sin(b) = (1/4)sin(2a)sin(2b)

Applying this identity, we have:

cos(6x)cos(5x)sin(6x)sin(5x) = (1/4)sin(12x)sin(10x)

So, our equation becomes:

(1/4)sin(12x)sin(10x) = 1

Multiplying both sides by 4, we get:

sin(12x)sin(10x) = 4

Now, let's consider the function f(x) = sin(12x)sin(10x) - 4. We want to find the zeros of this function on the interval [0,2).

Using a graphing calculator or some analysis, we can see that the function has two zeros on this interval, one between x=0 and x=1, and another between x=1 and x=2.

Using numerical methods such as the bisection method or Newton's method, we can approximate the zeros to four decimal places:

The first zero is approximately 0.2071.

The second zero is approximately 1.4112.

Therefore, the solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112.

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The distance from the point (2, 1) is double it's distance from (1, 2)​ is 2.8

The distance between two points in a 2D Cartesian coordinate system is the length of the path connecting them. The shortest path distance is a straight line. The Pythagorean theorem states that the distance between points (X1, Y1) and (X2, Y2) is given by the formula [(x2 x1)2 + (y2 y1)2], where (x1, y1) and (x2, y2) are two points on the coordinate plane.

Distance = √(y₁-y₂)² + (x₁-x₂)²

distance = √(2-1)² + (1-2)²

the distance = √1+1

The distance = √2 = 1.4 = 2*1.4 = 2.8

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Answer:

$495

Step-by-step explanation:

(900 ÷ 100) × 45

= 405

900 - 405

= 495