A vendor at a craft show sold items for $4.50, $6.00, and $7.50.
Altogether, the vendor sold 87 items for a total of $489. The vendor
sold five more items for $6.00 than for $7.50.

Let x = number of $4.50 craft items sold
Let y = number of $6.00 craft items sold
Let z = number of $7.50 craft items sold

Which system of equations could you use to determine how many
of each item were sold?


x + y + z = 489
z = y + 5
4.5x + 6y + 7.5z = 87

x + y + z = 87
y = z + 5
4.5x + 6y + 7.5z = 489

x + y + z = 489
y = z + 5
4.5x + 6y + 7.5z = 87

x + y + z = 87
z = y + 5
4.5x + 6y + 7.5z = 489

Answer:

The three numbers are 1, 2, and 4.

Step-by-step explanation:

\(x+y+z=7\\3x+1=z\\z+x=5\)

From these equations, we get:

\(x=1\\y=2\\z=4\)

Which fits all the equations we have written.

Answer:

b

Step-by-step explanation:

plato

If Henry decides to mow lawns then the opportunity cost would be - the chance to earn by working in a library

The correct answer is an option (B)

We know that,

Henry wants to get a job this summer.

He can either mow lawns or work in the local library.

if he decides to mow lawns, he would lost the chance to earn by working in a library.

This means, the opportunity cost is - the chance to earn by working in a library

Therefore, if Henry decides to mow lawns then the opportunity cost would be - the chance to earn by working in a library

The correct answer is an option (B)

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To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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Answer: 64 yards I think

Step-by-step explanation:

Answer: If it's just 8 feet wide, 64 yards, if 8 and 1/2, 68 yards.

Step-by-step explanation:

Answer:

Average Rate of Change = -0.4145

It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile

Step-by-step explanation:

In order to solve this problem, we can make use of the Average Rate of Change formula, which looks like this:

\(ARC=\frac{A(25)-A(20)}{25-20}\)

So we need to start by finding what A(25) is equal to, so we get:

\(A(25)= 0.0089(25)^{2}-0.0815(25)+22.3\)

so

A(25)=7.4875

next, we can find A(20)

\(A(20)=0.0089(20)^{2}-0.0815(20)+22.3\)

so we get:

A(20)=9.56

so now we can use the average rate of change formula:

\(ARC=\frac{A(25)-A(20)}{25-20}\)

\(ARC=\frac{7.4875-9.56}{25-20}\)

ARC=-0.4145

and It means that the amount of CO2 emitted per year will decrease by an averaage rate of 0.4145 (tons - gallon of gas)/mile

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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Pythagoras - Has a theorem named after him

Thales - Contributed to the five basic theorems of geometry

Pythagoras was a Greek philosopher, mathematician, and founder of the Pythagorean school of philosophy. He lived in the 6th century BCE on the Greek island of Samos and is known for his contributions to mathematics, geometry, music, and philosophy.

Pythagoras is most famous for the theorem that bears his name, the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is fundamental to the study of geometry and has applications in many fields, from architecture to physics.

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There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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Answer:

500 times

Step-by-step explanation:

Divide the thickness of a cat hair by the thickness of a human hair.

4.0 × 10^-1 / 8.0 × 10^-4 =

= 0.5 × 10^3

= 500

500 times

Answer:

x = 29.44

y = 34

Step-by-step explanation:

For this problem, we will simply use trigonometry to find the values of y and x for the given triangle.

The two trigonometric functions we will use are tangent and sine.

The general form for tangent is:

tan (Θ) = opposite / adjacent

The general form for sine is:

sin (Θ) = opposite / hypotenuse

For our given triangle, let's solve for x.

tan (30) = 17 / x

x * tan(30) = (17 / x) * x

x tan(30) = 17

x tan(30) * ( 1 / tan(30) ) = 17 * ( 1 / tan(30) )

x = 17 / tan(30)

x = 29.44

Now, let's solve for y.

sin (30) = 17 / y

y * sin(30) = (17 / y ) * y

y sin (30) = 17

y sin (30) * ( 1 / sin(30) ) = 17 * ( 1 / sin(30) )

y = 17 / sin(30)

y = 34

Hence, the values of x and y in our triangle are as follows:

x = 29.44

y = 34

Cheers.

Only the first statement is false. The rest are true statements about the Central Limit Theorem.

The Central Limit Theorem (CLT) is a fundamental theorem in probability and statistics which states that, given a sufficiently large sample size from a population with a given mean and standard deviation, the sampling distribution of the mean will be nearly normal, regardless of the shape of the original population distribution.

It is important to note that the first statement presented is false. Taking more samples from the population will not necessarily result in a more normal sampling distribution. The CLT does not guarantee that the sampling distribution will be normally distributed, only that it is more likely to be so as the sample size increases.

The second statement is true. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. The third statement is also true. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution.

Finally, the fourth statement is also true. The CLT states that the sampling distribution will be centered at the true population parameter. This means that the mean of the sampling distribution will be equal to the mean of the population.

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Answer:

X=69 degree

?= 50 degree

Step-by-step explanation:

exterior angle prop so 77+X =146

X=146-77

X=69

in sencond triangle

90+40+?=180

?=180-130

?=50

Answer:

midsegment = 23

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = \(\frac{18+28}{2}\) = \(\frac{46}{2}\) = 23

Answer:

B

Step-by-step explanation:

Standard deviation is the average distance away from the mean, thus B is correct

The required final answers of mixed fractions are 665/48, 259/45, 6095 / 28, 67/10.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

This expression can be evaluated by converting the mixed fraction to improper fractions and then performing the arithmetic operations.

1. \(2\frac{1}{3} +5\frac{5}{16} + \frac{2}{7}\)

= 7/3 + 85/16 + 2/7

=  665/48.

2. \(9\frac{5}{9} - 3\frac{2}{5}\)

= 86/9 - 17/5

= 259/45.

3. \(16\frac{3}{7} *13\frac{1}{4}\)

= 115/7 * 53/4

= 6095 / 28

4. \(16\frac{3}{4}\) ÷ \(2\frac{1}{2}\)

= 67/4 ÷ 5/2

= 67/10

Thus, required answers are 665/48, 259/45, 6095 / 28, 67/10.

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We have 4 expressions.

We have to find which ones give -4 as a result.

Answer:

Danielle earns $1.20 more than Mackenzie (per hour)

Step-by-step explanation:

To find out how much money per hour each person earns, you would divide the earinings by the number of hours;

Danielle: $36.80/4 = $9.20 per hour

MackKenzie: $50.40/6 = $8.40 per hour

To find out how much extra Danielle earns, you would subtract 8.40 from 9.20;

9.40 - 8.20 = $1.20

Thus, Danielle earns $1.20 more than Mackenzie per hour.

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

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

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{2}}}\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{6}(x-\stackrel{x_1}{2})\)

Answer:  y-2 = -6 (x-2)

Step-by-step explanation: Point slope form is this equation:

y-y1 = m (x-x1)

y1 is 2 because (2,2) ; The left 2 is x1 and the right 2 is y1.

(-1,20); The -1 is x2 and the 20 is y2.

If you use the equation above it helps a lot. I hope this helps you! :)

Answer:

12(1+3)

6(3+1)

12(4)

6(4)

48

24

answer = 2

The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

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Answer:314Step-by-step explanation:72+72+85+85 = 314

Answer:

AUB={1,2,3,4,5,7,8,9}

ALL THE NUMBERS WITHOUT REPEATING

AnB={5}

THE NUMBER THE HAVE IN COMMON

(AnB)n(BnC)={5}not too sure

CUD={1,3,6,7,8,10}

D

1) We need to remind ourselves of the Triangular inequality so that we can tackle this question:

Simply put, the sum of two sides must be greater than one of their sides.

2) Note that we were told that two of those legs have the size of 6 and 9

So, we can write out this:

3) Therefore, we can see that 3

Thus, the answer is D

Answer:

11

Step-by-step explanation:

The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.

Answer:

C

Step-by-step explanation:

it is a right triangle and the hypotanueses are congruent but we need a leg also to be congruent before we can say they are congruent so the answer is C.

If my answer helps please mark as brainliest.

Answer:

Step-by-step explanation:

I don't think there's enough information to do it.

HL is about the closest one, but the congruency marks only show that the hypotenuse is marked. You need something else.

AAS SAS ASA are all eliminated because no angle besides the right angle is given. The right angle is fine if the two sides making it up were marked. They are not.

Answer:

c=px8

Step-by-step explanation:

Answer:

5

20

5

Step-by-step explanation: srry im late

Answer:

First 5, Second 20, third 5.

Step-by-step explanation:

:D

Using conditional probability, it is found that there is a 0.6262 = 62.62% probability that the part is indeed defective.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

Event A: Positive test result.

Event B: Defective.

For the probability of a positive test result, we consider two scenarios.

Hence:

\(P(A) = 0.995(0.01) + 0.006(0.99) = 0.01589\)

The probability of a positive test result and being defective is:

\(P(A \cap B) = 0.995(0.01)\)

The conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.995(0.01)}{0.01589} = 0.6262\)

0.6262 = 62.62% probability that the part is indeed defective.

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Answer:

The depreciation tax shield for this project in year 4 is $178.24.

Explanation:

To calculate the depreciation tax shield for this project in year 4, we need to first determine the depreciation expense for year 4 using the MACRS three-year class life category and the double-declining balance (DDB) method.

From Table 12.8 on page 415 of the textbook, we can see that the depreciation rate for year 1 is 33.33%, for year 2 it is 44.45%, for year 3 it is 14.81%, and for year 4 it is 7.41%.

Using the DDB method, we can calculate the depreciation expense for each year as follows:

Year 1: Depreciation expense = $14,000 x 33.33% = $4,667

Year 2: Depreciation expense = ($14,000 - $4,667) x 44.45% = $3,554

Year 3: Depreciation expense = ($14,000 - $4,667 - $3,554) x 14.81% = $830

Year 4: Depreciation expense = ($14,000 - $4,667 - $3,554 - $830) x 7.41% = $557

The total depreciation expense over the four years is the sum of the individual year's depreciation expenses, which is:

$4,667 + $3,554 + $830 + $557 = $9,608

Now, we can calculate the depreciation tax shield in year 4. The depreciation tax shield is the amount of the depreciation expense that reduces the firm's taxable income, multiplied by the tax rate. In year 4, the depreciation tax shield is:

Depreciation tax shield = Depreciation expense in year 4 x Tax rate

Depreciation tax shield = $557 x 32% = $178.24

Therefore, the depreciation tax shield for this project in year 4 is $178.24.

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U thought this was a professional answer?!!!!??????

You're wrong!!!!!!!!!!!!!!!!!

But the answer is correct though...

:))

PEW PEW PEW

Bing Chilling

It's over...

No more to read

Happy birthday if it's ur birthday...

Have a nice day my king:)