A principal wants to buy new sports uniforms for the basketball team. Eachuniform costs $9.45 and there is a shipping charge of $7.95 for the entire order. Thereis no tax on the order. The total charge of the principal's order is less than $120.Which inequality can be used to determine the greatest number of sports uniforms, theprincipal orders?(A) 9.45t + 7.95< 120(B) 7.95t + 9.45 < 120(C) 9.45t + 7.95 > 120(D) 7.95t+ 9.45 > 120

\( \frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2} \)

1/8 is not equal to 1/2

\( \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4} \)

3/8 is not equal to 1/2

5/8 is not equal to 1/2

\( \frac{6}{8} = \frac{6 \div 2}{8 \div 2} \\ \frac{3}{4} \)

7/8 is not equal to 1/2

SO ONLY 4/8 IS EQUAL TO 2 QUARTERS

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

can you zoom in on my pic more or no does it say 1/z

Answer:

Option A. Reciprocal

Answered by GAUTHMATH

The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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The best statement that describes the strategy for estimating the perimeter of the figure (please see the attached diagram) is the option;

Ad the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

An estimate is an approximation of a true value, which is a value that is close to the actual value of the measured quantity.

Please find attached a diagram of the possible figure created with MS Word

The length of the side of the sides of the possible figure in the figure, obtained from a similar question on the internet are;

Base length = 5 units

Height = 4 units

The figure has a diagonal side which is 4 units wide and 2 units tall.

The length of the slant side, found using Pythagorean theorem can be obtained as follows; Length = √(4² + 2²) = 2·√5 ≈ 5

The correct option is therefore to add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall

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The equation representing the given linear function in the slope-intercept form is 2 = 4x + 4.

So, the linear function in the slope-intercept form will be:

Take two coordinates as follows:

(2, 4) and (3, 8)

Now, insert values and calculate:

Now, the equation formula: y = MX + b

Take (2, 4):

Therefore, the equation representing the given linear function in the slope-intercept form is 2 = 4x + 4.

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r = - 0.98754

Answer:

Slope = - 0.7120

SE = 1.295

Step-by-step explanation:

Given the data:

0 | 33.3

0 | 31.0

3 | 29.8

3 | 27.8

6 | 28.0

6 | 29.0

10 | 25.5

10 | 23.8

20 | 18.3

20 | 15.5

30 | 11.7

Using the relation to Obtian the slope :

Slope, b = r(Sy/Sx)

r = correlation Coefficient ; Sy = standard deviation of Y - values ; Sx = standard deviation of X-values

r = - 0.98754

Slope, b = - 0.98754(7.8471 / 10.884) = - 0.7120

SE = √SSresidual / df

df = n - 2 = 12 - 2 = 10

SSresidual = 16.7812

SE = √(16.7812/ 10)

SE = 1.295

Answer:

x = five over two and x = −3

Step-by-step explanation:

Let's solve your equation step-by-step.

2x2+x=15

Step 1: Subtract 15 from both sides.

2x2+x−15=15−15

2x2+x−15=0

Step 2: Factor left side of equation.

(2x−5)(x+3)=0

Step 3: Set factors equal to 0.

2x−5=0 or x+3=0

x=5/2 or x=−3

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

Answer:

Step-by-step explanation:

Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.

The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

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Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Answer:

no

Step-by-step explanation:

Answer:

- Erkan is out of control and kicks and rants at the nursing staff.

- Michelle is a young high school girl and feels that everyone mistrusts her due to her youth.

- Michelle wears a football jersey and jeans to her internship at the nursing home.

S

The statements that development the theme mentioned are; 2. Michelle join Erkan in his own world instead of avoiding him. 3. Erkan's face brightens in a smile as soon as Michelle rushes to his side.

Contingency is a statement in which there are some true and some false values for every value of its propositional variables.

From the given five statements presented under the problem, the two that present development on the theme mentioned at the beggining are to be considered correct:

Second Statement implies that Michelle learned enough from Erkan's history and personality, and despite any possible misconceptions, she ended up sympathizing with him. So, a hanging bond was created from Michelle's side.

Statement 3 has a connection with the statement 2.

Statements 1 and 5 cannot be considered correct, the lack of confidence Erkan demonstrates towards the people surrounding him at the nursing home.

Statement 4 that presents no bond creation, rather an event occurred during Erkan's lifetime.

The statements that development the theme mentioned are; 2. Michelle join Erkan in his own world instead of avoiding him. 3. Erkan's face brightens in a smile as soon as Michelle rushes to his side.

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Answer:

48/24

Step-by-step explanation:

You didn't say which one is line BC so I'm going to give you the answer 48 for the entire line but if you are asking for the middle point to end point then it is 24.

Answer:

Step-by-step explanation:

Before we can calculate the standard deviation of the dataset, we need to get the mean value first.

mean = sum of the values/total number given

mean = -8+2+2+4+15/5

mean = 15/5

mean (xbar) = 3

For ungrouped data:

Variance S²=  ∑(xi-xbar)²/N-1

xi are the individual values

xbar is the mean value = 3

N is the total number in the dataset = 5

Variance = (-8-3)²+(2-3)²+(2-3)²+(4-3)²+(15-3)²/5-1

S² = (-11)²+(-1)²+(-1)²+(1)²+(12)²/4

S² = (121+1+1+1+144)/4

S² = 67

Hence the variance of data sample is 67.00

Standard deviation is the square root of the variance.

√S² = Standard deviation

√67 = Standard deviation

Standard deviation = 8.185

Standard deviation ≈ 8.19 (to 2 decimal place)

The monthly payments over a period of 5 years is $214.05.

A fixed-rate mortgage is a home loan option with a specific interest rate for the entire term of the loan. Essentially, the interest rate on the mortgage will not change over the lifetime of the loan and the borrower's interest and principal payments will remain the same each month.

Given that, a family borrows $12,843 for an addition to their home.

The loan is to be paid off in monthly payments over a period of 5 years

We know that, 5 years = 60 months

Now, monthly payment = Total money/Number of months

= 12,843/60

= $214.05

Therefore, the monthly payments over a period of 5 years is $214.05.

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Answer:

3 30 page printers, 10 70 page printers

Step-by-step explanation:

x + y = 13

40x+70y = 820

Solving for y in first equation gives: y = 13 - x

Plug into second equation: 40x + 70(13 - x) = 820

40x + 910 - 70x = 820

-30 x = -90

x = 3

Plug into original equation: 3 + y = 13

y must = 10.

So, the company owns 3 thirty page presses, and 10 70 page presses,

Step-by-step explanation:

hope this will help you......

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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We should order 70 hats and 140 pairs of sunglasses to lose the least amount of money in the sales promotion.

What is linear optimization?

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

This is a linear optimization problem that can be solved using the graphic method.

To begin, we can set up the problem as follows:

Let x be the number of hats and y be the number of pairs of sunglasses.

The constraints are:

y = 2x (because for every 2 hats sold, 1 pair of sunglasses is sold)

y <= 100 (because the supplier can only provide 100 pairs of sunglasses)

x + y >= 210 (because you want to sell at least 210 items in total)

x, y >= 0 (because the number of items sold cannot be negative)

The objective function is: -3x - 2y (because you lose $3 on every hat sold and $2 on every pair of sunglasses sold)

To graph the constraints, we can start by plotting the inequality y <= 100. This creates a line that goes from the origin (0,0) to (50,100) and is shaded in below the line. Next, we can plot the inequality x+y >= 210 which creates a line that goes from (0, 210) to (210, 0) and is shaded in above the line.

Finally, we can plot the equation y = 2x, which represents the relationship between the number of hats and sunglasses sold.

The feasible solution for this problem is the point where the lines intersect and that lies within the feasible region. In this case, the point where the three lines intersect is (70, 140) which is the optimal solution.

Therefore, you should order 70 hats and 140 pairs of sunglasses to lose the least amount of money in the sales promotion.

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The quotient of a number x and two tenths is 5x

Quotient is defined as the quantity derived from the division of two numbers.

From the information given, we are to find the the quotient of;

The quotient is written thus;

= x/ 2/ 10

Take the inverse of the denominator and multiply

= x × 10/ 2

= 10x/ 2

find common divisor

= 5x

Thus, the quotient of a number x and two tenths is 5x

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Answer:

16 for the first one. each segment is 4

40 for the second. each segment is 8

Answer:

0, 4, 8, 12, 16

8, 16, 24, 32, 40, 48

Step-by-step explanation:

The first number line has 6 parts. 24÷6=4. Each vertical line will increase by 4.

So starting at 0, the parts of the number line are:

0, 4, 8, 12, 16, 20, 24

The specific part being asked for is 0, 4, 8, 12, 16

The second number line has 8 parts. 64÷8=8. Each vertical line will increase by 8.

Starting at 0, the parts of the number line are:

0, 8, 16, 24, 32, 40, 48, 56, 64

The specific part being asked for is 8, 16, 24, 32, 40, 48

\(\\ \sf\longmapsto 3x^2+5x-8-(2x^2-4x+3)\)

\(\\ \sf\longmapsto 3x^2+5x-8-2x^2+4x-3\)

\(\\ \sf\longmapsto 3x^2-2x^2+5x+4x-8-3\)

\(\\ \sf\longmapsto x^2+9x-11\)

Answer:

(3×2+5x-8)-(2×2-4x-3) = (6+5x-8)-(4-4x-3)

= 6+5x-8-4+4x+3

= -3+9x

The value of x in the given set triangles are:

1) x=17.5

2) x=48

3) x= 8

4) 24.5

5) x=11

6) x=9

What is Triangle Proportionality Theorem?

If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides.

1) According to Triangle Proportionality Theorem,

from given fig 1,

          \(\frac{14}{12} =\frac{x}{15} \\\\\frac{7}{6} =\frac{x}{15} \\\\x= 17.5\)

2) From fig 2,

          \(\frac{x}{18} =\frac{56}{21} \\\\x=48\)

3) From fig 3,

           \(\frac{x}{36} =\frac{10}{45} \\\\\frac{x}{36} =\frac{2}{9} \\\\x=8\)

4) From fig 4,

          \(\frac{6}{21}=\frac{7}{x} \\\\6x=7*21\\\\x=24.5\)

5) From fig 5,

         \(\frac{30}{x+7} =\frac{25}{15} \\\\\frac{30}{x+7} =\frac{5}{3} \\\\x=11\)

6) From fig 6,

         \(\frac{6}{21}=\frac{x-1}{3x+1} \\\\ 18xx+6=21x-21\\\\3x=27\\\\x=9\)

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Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

First set of questions is

2.05 and 14.61

The second set is

D. If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Step-by-step explanation:

The zeroes of the quadratic function is x = 2.05 and x = 14.61

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

y = -6x² + 100x + 180   be equation (1)

where x = selling price of each soccer ball

y = daily profit from soccer balls

On factorizing the equation , we get

when y = 0

6x² - 100x - 180 = 0

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = [ 100 ± √ ( 100 )² - 4 ( 6 ) ( 180 ) ] / 12

x = [ 100 ± √ ( 10000 ) - 4320 ) ] / 12

x = [ 25 ± √355 ] / 3

So , the two values of x are x = 2.05 and x = 14.61

Hence , the zeroes of the function are 2.05 and x = 14.61

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Answer:

answer is 3 3/20