1. In Exercise 1 of Section 3.3, indicate whether the given vectors form a basis for R 2.
1 , -1
2 -2
3 , -2 , 0
1 4 1 1 , 2
1 -1

Step-by-step explanation:

If I=Prt

I is interest earned

P is principal

R is the interest rate

T is time in years

Then substitute the values into the equation

Plug into your calculator

I= 100 x 6% x 3 = 18

Answer for the first one is $18

For the others, it requires you to rearrange the equation.

Good luck!

If a large diamond with a mass of 4289.6 grams was recently discovered in a mine and the density of the diamond is 3.51 grams over centimeters cubed, the volume is 1221.9 cm³.

To find the volume of the diamond, we need to use its mass and density. The density of the diamond is given as 3.51 grams per cubic centimeter. This means that every cubic centimeter of diamond has a mass of 3.51 grams.

We can use this information to find the volume of the diamond by dividing its mass by its density. Plugging in the given values, we get:

Volume = Mass / Density

Volume = 4289.6 g / 3.51 g/cm³

Volume = 1221.86 cm³

This means that the diamond has a volume of 1221.86 cubic centimeters. However, the question asks us to round the answer to the nearest hundredth, so we round this value to: Volume = 1221.9 cm³

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The constraints as a system of linear inequalities include the following;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640

75x + 60y ≤ 12,900

The solution set for the system of linear inequalities is shown in the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640.

75x + 60y ≤ 12,900

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Answer:   [tex]\frac{10}{100}[/tex]× 100

Step-by-step explanation:

Answer:

10/100 = 10%

Step-by-step explanation:

10/100 = 0.1

0.1 * 100 = 10%

Answer:

Step-by-step explanation:

2.02

x=21 so replace x with 21

3(21)+y/z

then do the same with y and z

3(21)+36/49

63+36/49

99/49

SOLUTION 2.02

[tex]36 cm^3[/tex] of pure alcoh ol must be added to the [tex]10 cm^3[/tex] of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.

What is Algebraic expression ?

Algebraic expression can be defined as combination οf variables and constants

Let's first calculate the amount  of pure alcohol in the 8% solution:

Amount of pure alcohol = 8%  of [tex]10 cm^3 = 0.08 x 10 cm^3 = 0.8 cm^3[/tex]

N ow, let's  assume [tex]x cm^3[/tex]of pure alcohol must be added to the 10 cm^3 of the 8% solution to obtain a total volume of [tex]10 + x cm^3[/tex] of an 80% solution. The amount of pure alcohol in the final solution would be:

ο[tex](10 + x) cm^3 = 0.8 (10 + x) cm^3[/tex]

Since we started with [tex]0.8 cm^3[/tex]of pure alcohol and we want to end up with  

[tex]0.8 (10 + x) cm^3[/tex], we can set up the following equation:

[tex]0.8 + x = 0.8 (10 + x)[/tex]ο

Simplifying and solving for x, we get:

[tex]0.8 + x = 8 + 0.8x[/tex]

[tex]0.2x = 7.2[/tex]

[tex]x = 36[/tex]

Therefore, [tex]36 cm^3[/tex] of pure alcohol must be added to the [tex]10 cm^3[/tex]of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.

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Answer:

36cm^3

Step-by-step explanation:

The comparison operator (<) can be overloaded for a class as a function in all three ways: member, friend, and global (non-member, non-friend). Therefore, the correct answer is e. all three (a, b, and c).

When overloading the comparison operator (<) as a member function, it is defined within the class and has access to all the members and functions of the class.

When overloading the comparison operator (<) as a friend function, it is defined outside of the class but is given access to all the members and functions of the class.

When overloading the comparison operator (<) as a global (non-member, non-friend) function, it is defined outside of the class and does not have access to the members and functions of the class. However, it can still be used to compare objects of the class by using the accessor functions defined for the class.

The comparison operator (<) can be overloaded for a class as a function in all three ways: member, friend, and global (non-member, non-friend).

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For the given fraction, "Yes" for 8/18 and 12/27, and "No" for 20/36 and 24/45.

The first step in determining whether fractions are equivalent is to simplify them. This involves finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by it. Simplifying fractions allows us to express them in their simplest form, making it easier to compare them to other fractions.

Let's start by simplifying the given fractions:

20/36 = 5/9

8/18 = 4/9

24/45 = 8/15

12/27 = 4/9

As we can see, two of the fractions simplify to 4/9, while the other two do not.

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Answer:

90$

Step-by-step explanation:

We need to find 15% of the number 600:

[tex] \frac{600 \times 15\%}{100\%} = 90 [/tex]

So, the answer is 90$

For a randomly chosen family in the suburb, the probability of having an income between $60,000 and $72,000 is 40%. This is because 40% of all families in the suburb have incomes above $72,000, and the median income for all families in the suburb is $60,000.

Therefore, the probability of having an income between [tex]$60,000[/tex] and $72,000 is 40%.

This information can also be interpreted in a graphical representation. The graph will have a vertical line at $60,000 and a horizontal line at 40%. The area between these two lines will represent the probability of having an income between $60,000 and $72,000, which is 40%.

In conclusion, for a randomly chosen family in the suburb, the probability of having an income between $60,000 and $72,000 is 40%.

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The algebraic expressions that are polynomials are:

1. 2x³ -/-/-

2. 0x³y - 3x² + 6x

3. -x + √6

Polynomials are a type of algebraic expression that consists of variables and coefficients, combined using mathematical operations of addition, subtraction, and multiplication, and non-negative integer exponents. The term "poly" means many, and "nomial" means term. Hence, a polynomial is a sum of many terms.

Algebraic expressions are mathematical expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used in algebra to represent relationships between variables and to solve mathematical problems.

The algebraic expressions that are polynomials are:

1. 2x³ -/-/- (a polynomial of degree 3)

2. 0x³y - 3x² + 6x (a polynomial of degree 3)

3. -x + √6 (a polynomial of degree 1)

The expressions that are not polynomials are:

1. y² + 5y -√3 (not a polynomial because it contains a square root)

2. 02-√4x (not a polynomial because it contains a square root)

3. 0-32³-12-2²+1 (not a polynomial because it contains a negative exponent)

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The exact value of sin−1(cos(1013​π)) is sin−1(1 / (2sin(1013π) - cos(1013π) + 1)).

To find the exact value of sin−1(cos(1013​π)), we need to use the identity sin^2(x) + cos^2(x) = 1. Since sin−1(cos(1013​π)) is an angle whose sine is cos(1013​π), we can let that angle be x: sin(x) = cos(1013π).Let's find the sine of x using the identity sin^2(x) + cos^2(x) = 1:sin^2(x) + cos^2(x) = 1sin^2(x) + (cos(1013π))^2 = 1sin^2(x) + cos^2(1013π) = 1sin^2(x) + sin^2(π/2 - 1013π) = 1Now we need to simplify sin^2(π/2 - 1013π):sin^2(π/2 - 1013π) = sin^2(π/2)cos^2(1013π) - 2sin(π/2)cos(1013π)sin(1013π/2) + sin^2(1013π/2)= 1(cos(1013π))^2 - 2sin(1013π/2)cos(1013π) + 0= cos^2(1013π) - 2sin(1013π)cos(1013π)= cos(1013π)(cos(1013π) - 2sin(1013π))Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite sin^2(x) as 1 - cos^2(x):sin^2(x) + cos^2(x) = 11 - cos^2(x) + cos^2(1013π) = 11 - cos(1013π)(cos(1013π) - 2sin(1013π)) + cos^2(1013π) = 1cos(1013π) - cos(1013π)^2 + 2sin(1013π)cos(1013π) = 1cos(1013π) + cos(1013π)(2sin(1013π) - cos(1013π)) = 1cos(1013π)(2sin(1013π) - cos(1013π) + 1) = 1cos(1013π) = 1 / (2sin(1013π) - cos(1013π) + 1)Therefore, the exact value of sin−1(cos(1013​π)) is sin−1(1 / (2sin(1013π) - cos(1013π) + 1)).

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Answer:

hey will you be my friend

I yes then text me

The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line b are (- 1, 1) and (- 2, 3).

Now,

Since, The equation of line passes through the points ( (- 1, 1) and (- 2, 3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - 1)) / (- 2 + 1)

m = 2 / - 1

m = - 2

Thus, The equation of line with slope - 2 is,

⇒ y - 1 = - 2 (x + 1)

⇒ y - 1 = - 2x - 2

⇒ y = - 2x - 1

Therefore, The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

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Answer:

this is the answer to that problem

The standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).

Standard deviation (σX) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. Here is how to compute it from the given data:\begin{tabular}{cc} \hline Number of Hours & Frequency \\ \hline 0 & 127 \\ 1 & 176 \\ 2 & 348 \\ 3 & 252 \\ 4 & 328 \\ 5 & 239 \\ 6 & 139 \\ 7 & 27 \\ 8 & 60 \\ \hline Total & 1696 \end{tabular}(b) Compute the standard deviation σX​. Round the answer to at least three decimal places.The formula to use is:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}}\]where:σX = standard deviation∑ = sum off = frequencyxi = value of i-th datan = total number of data\[\overline{x} = \frac{\sum fx}{n}\]is the sample mean, which we must calculate first.\[\overline{x} = \frac{\sum fx}{n} = \frac{0\cdot127 + 1\cdot176 + 2\cdot348 + 3\cdot252 + 4\cdot328 + 5\cdot239 + 6\cdot139 + 7\cdot27 + 8\cdot60}{1696} \approx 2.7875\]Substituting into the standard deviation formula:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}} = \sqrt{\frac{0\cdot(127 - 2.7875)^2 + 1\cdot(176 - 2.7875)^2 + 2\cdot(348 - 2.7875)^2 + 3\cdot(252 - 2.7875)^2 + 4\cdot(328 - 2.7875)^2 + 5\cdot(239 - 2.7875)^2 + 6\cdot(139 - 2.7875)^2 + 7\cdot(27 - 2.7875)^2 + 8\cdot(60 - 2.7875)^2}{1696}} \approx 1.936\]Therefore, the standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).

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Existence and uniqueness of solutions to systems of differential equations depend on the number of equations and the order of each equation. For example, a system of two first-order equations has a unique solution, while a system of three first-order equations may not have a unique solution.

Previously, we considered the scalar differential equation, which is a single differential equation involving only one independent variable. In this case, the solution to the equation is unique. This is because there is only one equation and only one variable, so the solution must be unique for a given set of initial conditions.

For a system of differential equations, the existence and uniqueness of solutions depend on the number of equations and the order of each equation.

Systems of differential equations with higher order equations or more equations than unknowns may not have a unique solution. On the other hand, if there are more unknowns than equations, then there is always a unique solution. To find the solution, the equations must be solved simultaneously.

In conclusion, A scalar differential equation always has a unique solution.

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Akio is a public communication specialist with skill sets to influence and raise awareness for public.

What do you mean by public communication specialist?

Specialists in public-relations develop and uphold a positive public image for the people, groups, or organisations they represent. To influence how the public perceives their clients and to raise awareness of each client's efforts and objectives, they prepare press releases and create social media strategies.

Public relations, information output, and media requests are handled by communications specialists. They can also plan an organization's social media or advertising campaigns.

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Answer:

10. To find the area of rhombus ABCD, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

We need to find the length of both diagonals. Since the diagonals of a rhombus are perpendicular and bisect each other, we can use the Pythagorean theorem to find the length of each diagonal.

AC is one diagonal, AB is a side of the rhombus, and BD is the other diagonal divided by 2 (since BD bisects AC):

BD = AC/2 = 10/2 = 5 cm

Using the Pythagorean theorem with AC and BD:

AC^2 = AB^2 + BD^2

AC^2 = 13^2 + 5^2

AC^2 = 169 + 25

AC^2 = 194

AC = sqrt(194) ≈ 13.93 cm

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

    = (13.93 x 5) / 2

    ≈ 34.83 cm^2

Therefore, the area of rhombus ABCD is approximately 34.83 cm^2.

11. We know that the area of rhombus ABCD is 96 cm^2, and that BD is 8 cm. To find the length of AC, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

Solving for diagonal 1 (AC):

AC = (2 x Area) / BD

  = (2 x 96) / 8

  = 24 cm

Therefore, the length of AC is 24 cm.

12. We know that AB is a side of the rhombus and that AB = 16 m. We also know that mZABD = 60 degrees. We can use trigonometry to find the length of the diagonals.

First, we can find the length of AD using the law of cosines:

AD^2 = AB^2 + BD^2 - 2(AB)(BD)cos(mZABD)

AD^2 = 16^2 + (2x)^2 - 2(16)(2x)cos(60)

AD^2 = 256 + 4 - 32x

AD^2 = 260 - 32x

AD = sqrt(260 - 32x)

Then, we can find the length of AC using the law of sines:

AC / sin(mZBAD) = AD / sin(mZABD)

AC / sin(120) = AD / sin(60)

AC = (AD x sin(120)) / sin(60)

AC = (sqrt(260 - 32x) x sqrt(3)) / 2

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

    = [(sqrt(260 - 32x) x sqrt(3)) / 2] x 8 / 2

    = 2(sqrt(260 - 32x) x sqrt(3))

    ≈ 67.29 m^2

Therefore, the area of rhombus ABCD is approximately 67.29 square meters.

13. We know that the perimeter of the rhombus is 20 mm, so each side is 5 mm. We also know that AC is one of the diagonals. To find the length of the other diagonal, we can use the Pythagorean theorem.

Let x be half the length of the other diagonal:

AC^2 = (2x)^2 + 5^2

x^2 = (AC^2 - 25) / 4

x = sqrt((AC^2 - 25) / 4)

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

    = (AC x 2x) / 2

    = xAC

    = sqrt((AC^2 - 25) / 4) x AC

    ≈ 19.80 mm^2

Therefore, the area of rhombus ABCD is approximately 19.80 square millimeters.

Answer:

this is actually about derivatives,

the answer would be simply 10x-6

Kayla would ultimately spend $210.91 + $14.76 = $225.67 for all the clothing items, including sales tax.

To determine if Kayla's budget will be enough to purchase all the clothing items listed after sales tax is applied, we need to calculate the total cost of the items first.

The cost of 2 T-shirts would be 2 x $9.98 = $19.96.

The cost of 3 dresses would be 3 x $24.99 = $74.97.

The cost of 1 pair of pants would be $25.99.

The cost of 1 pair of shoes would be $89.99.

Therefore, the total cost of the clothing items is $19.96 + $74.97 + $25.99 + $89.99 = $210.91.

Next, we need to add the sales tax rate of 7% to the total cost to find the final price that Kayla would pay.

7% of $210.91 = $14.76

Therefore, the final price that Kayla would pay for all the clothing items, including sales tax, is $210.91 + $14.76 = $225.67.

Since Kayla's budget is $200, she would not have enough money to purchase all of the clothing items listed after sales tax is applied.

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The customer will pay R108 for the screwdriver set.The trader bought a screwdriver set for R90 and added 20% to the cost price for profit and expenses. To calculate the amount a customer will pay for the screwdriver set, we need to add the profit and expenses to the cost price.

First, let's calculate the profit and expenses added by the trader. Since the trader added 20% to the cost price, the profit and expenses will be:

20% of R90 = 0.2 x R90 = R18

Now, we can calculate the selling price of the screwdriver set by adding the cost price and the profit and expenses:

Cost price = R90

Profit and expenses = R18

Selling price = Cost price + Profit and expenses = R90 + R18 = R108

Therefore, the customer will pay R108 for the screwdriver set.

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[tex] \bf Question :- \\ [/tex]

what is the value of expression

when g=4 and h=2

[tex] \bf Solution :- \\ [/tex]

[tex] \longrightarrow \: \: \frac{1}{4} (16 + g) - h \\ \\ \longrightarrow \: \: \frac{1}{4} (16 + 4) - 2 \\ \\ \longrightarrow \: \: \frac{1}{{ \cancel{4} }} \times( \cancel{ 20)} - 2 \\ \\ \longrightarrow \: \: 1 \times 5 - 2 \\ \\ \longrightarrow \: \: 1 \times 3 \\ \\ \longrightarrow \: \: 3 \\ [/tex]

Henceforth, Option c is the required answer.

Answer:

Step-by-step explanation:

We can start by using the logarithmic rule that states:

log a (mn) = log a (m) + log a (n)

And also the property:

log a (b^c) = c*log a (b)

With these rules, we can simplify the given expression as follows:

log4 n = 1/4 log4 81 + 1/2 log4 25

log4 n = log4 81^(1/4) + log4 25^(1/2) (using the above properties)

log4 n = log4 (3^4)^(1/4) + log4 (5^2)^(1/2) (81 = 3^4 and 25 = 5^2)

log4 n = log4 3 + log4 5 (using the rule log a (b^c) = c*log a (b))

log4 n = log4 (3*5) (using the rule log a (mn) = log a (m) + log a (n))

log4 n = log4 15

Therefore, the solution to the equation log4 n=1/4 log4 81 + 1/2 log4 25 is:

n = 15

The null hypothesis and alternative hypothesis for the population mean µ are identified for the given research hypotheses.

The null hypothesis and alternative hypothesis for the population mean µ are as follows:a) H0: µ ≥ 14; H1: µ < 14b) H0: µ ≤ $4.50; H1: µ > $4.50c) H0: µ ≥ $5000; H1: µ < $5000d) H0: µ = 60; H1: µ ≠ 60 Research hypotheses that are to be substantiated by sample data are as follows:a) The mean time a health insurance company takes to pay claims is less than 14 working days.Null hypothesis H0: µ ≥ 14 Alternative hypothesis H1: µ < 14b) The average person watching a movie at a local multiplex theater send over $4.50 on refreshments.

Null hypothesis H0: µ ≤ $4.50 Alternative hypothesis H1: µ > $4.50c) The mean hospital bill for birth in the city is less than $5000.Null hypothesis H0: µ ≥ $5000 Alternative hypothesis H1: µ < $5000d) The mean time between purchases of a brand of mouthwash by loyal customers is different from 60 days.Null hypothesis H0: µ = 60 Alternative hypothesis H1: µ ≠ 60 Hence, the null hypothesis and alternative hypothesis for the population mean µ are identified for the given research hypotheses.

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The value is x in the equation is -2

The value of y in the equation is -8.67

5x - 3y= 16...........equation 1

4x + 5x= -2..........equation 2

Multiply equation 1 by 4 and equation 2 by 5

20x - 12y= 64

20x + 25x= -10

-37x= 74

x= -74/37

x= -2

Substitute -2 for x in equation 1

5x - 3y= 16

5(-2) - 3y= 16

-10 -3y= 16

-3y= 16+10

-3y= 26

y= -26/3

y= -8.67

Hence the value of x is -2 and the value of y is -8.67

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Answer:

What does the circled part of the picture represent?

A)  a point

B)  a line

C)  line segment

D)  ray

Step-by-step explanation:

it is a btw

The Eiffel Tower is approximately 919 feet tall to the nearest foot.

We can use trigonometry to solve this problem.

Let's assume that the height of the Eiffel Tower is h feet.

From the problem, we know that Mai is 80 feet away from the base of the tower and looking up at an angle of 85.7 degrees. We can use the tangent function to relate the height of the tower to the angle and distance:

tan(85.7) = h/80

We can solve for h by multiplying both sides by 80:

h = 80 × tan(85.7)

Using a calculator, we get:

h ≈ 919.4 feet

Therefore, the Eiffel Tower is approximately 919 feet tall to the nearest foot.

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The interval of times that represent the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].

Using the empirical rule or the elliptical rule, we know that in a normal distribution:

In this case, we want to find the interval of times that represents the middle 99.7% of Aaron's finishing times, which means we need to find the range of values that fall within three standard deviations of the mean.

So, using the formula for finding the interval of values within k standard deviations of the mean:

lower bound = mean - k * standard deviation

upper bound = mean + k * standard deviation

where k = 3 for this problem, we get:

lower bound = 80 - 3 * 2.5 = 72.5

upper bound = 80 + 3 * 2.5 = 87.5

Therefore, the interval of times that represents the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].

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Answer: First 2 questions are 12.5% and the third is 25%

Step-by-step explanation: Add up all the possibilities then take the desired possibility and divide by the total possibilities then multiply by 100