A system of equations is shown below.
y=2/3x−5
y=1/2x+3

How many solutions does the system have?
A.2 solutions
B.no solutions
C.infinite solutions
D.1 solution

Consider that X is the staff so at tinier location while Y is workforce at the origin. 9 people are employed at tiny site, compared to 24 at larger location (s).Is the right answer.

X + Y = 33

It is assumed that two times the number of employees at the larger location is three times the number at the smaller location. The equation for this is as follows:

2Y = 5X + 3

Because we already know that X + Y = 33, we can write it as X = 33 - Y.

Let us now plug X into the above equation.

2Y = 5*(33 - Y) + 3

2Y = 165 - 5Y + 3

7Y = 168

Y = 168 / 7

Y = 24

Let us now compute the value of X.

X + Y = 33

X + 24 = 33

X = 9

The smaller location employs 9 people, while the larger location employs 24 people (s).

To know more about equation click here

brainly.com/question/649785

#SPJ4

Answer:

$7500

Step-by-step explanation:

So to find mean the formula is total divided by no. of items or values so therefore the total no. of people is 310+390+380+420 which is 1500 people and if one ticket is $20 ,1500 tickets is 1500 multiplied by 20 which is $30,000 and the mean of one night would by 30,000 divided by 4 nights which is $7500 per night.Hope this helped!

Herefore, the vertices of the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ are X''(-2, -1), Y''(0, -1), and Z''(0, 1).

First, we need to perform a reflection over the x-axis and then a translation of 2 units to the left and 4 units up. This is the transformation T−2,4.

Next, we need to perform a rotation of 180 degrees about the origin. This is the transformation RO,180°.

We can apply these transformations to each vertex of the first triangle ΔXYZ to obtain the coordinates of the final image.

Applying T−2,4 to each vertex:

T−2,4(X) = (2, 5) → reflection over x-axis → (2, -5) → translation 2 units left and 4 units up → (0, -1)

T−2,4(Y) = (2, 3) → reflection over x-axis → (2, -3) → translation 2 units left and 4 units up → (0, 1)

T−2,4(Z) = (4, 3) → reflection over x-axis → (4, -3) → translation 2 units left and 4 units up → (2, 1)

Applying RO,180° to each vertex:

RO,180°(0, -1) = (0 × cos(180°) - (-1) × sin(180°), 0 × sin(180°) + (-1) × cos(180°)) = (0, 1)

RO,180°(0, 1) = (0 × cos(180°) - 1 × sin(180°), 0 × sin(180°) + 1 × cos(180°)) = (0, -1)

RO,180°(2, 1) = (2 × cos(180°) - 1 × sin(180°), 2 × sin(180°) + 1 × cos(180°)) = (-2, -1)

To more about corordinate visit :https://brainly.com/question/20282507

#SPJ1

Answer:

x is (-4,-1)

y is (-4,1)

z is (-6,1)

Step-by-step explanation:

Answer:

172.72 cm

Step-by-step explanation:

5 feet 8 inches in cm = [(5×12)+8] x 2.54 = 68 x 2.54 = 172.72 cm

The expression −2⋅[4x+1(−2)] is d. -16.

To simplify the expression −2⋅[4x+1(−2)], we first need to evaluate the expression inside the square brackets:

4x + 1(-2) = 4x - 2

Then we can substitute this back into the original expression:

−2⋅[4x+1(−2)] = −2⋅(4x - 2)

Using the distributive property, we can multiply -2 by each term inside the brackets:

−2⋅(4x - 2) = -8x + 4

Therefore, the answer is d. -16.

Learn more about expression here:https://brainly.com/question/1859113

#SPJ1

The solution set of the given homogeneous system in parametric vector form is x = (0, 0, t), where t is a real number

Vectors are an important mathematical tool for representing complex data and equations. In this problem, we are given a homogeneous system of equations and asked to write the solution set in parametric vector form.

The homogeneous system consists of three equations: 3x₁ + 3x₂ + 6x₃ = 0, -6x₁ - 6x₂ - 12x₃ = 0, and -4x₂ + 4x₃ = 0. To solve this system, we need to use linear algebra techniques, such as Gaussian elimination, to find the solution set.

By using Gaussian elimination, we can reduce the system to a simpler system, which has the form x₁ = 0, x₂ = 0, and x₃ = t, where t is a real number. This can be written as a parametric vector form as x = (0, 0, t).

To know more about system of equations here.

https://brainly.com/question/12895249

#SPJ4

Answer:

no solution

Step-by-step explanation:

7 | y + 6 | + 3 < - 18 ( subtract 3 from both sides )

7 | y + 6 |  < - 21 ( divide both sides by 7 )

| y + 6 | > - 3

the absolute value function cannot be negative

thus the equation has no solution

5/6 can be expressed as 83% in percentage form.

Percentages are a way of expressing a fraction as a portion of 100. This makes it easier to compare fractions and understand their relative sizes. In this case, we will be converting the fraction 5/6 into a percentage.

To convert 5/6 into a percentage, we need to first divide the numerator (top number) by the denominator (bottom number) and then multiply the result by 100. This will give us the percentage equivalent of the fraction.

So, let's do the math:

5 ÷ 6 = 0.83333...

We can round this to two decimal places, giving us:

0.83

Now, we need to multiply this by 100 to convert it into a percentage:

0.83 × 100 = 83%

It's important to remember that percentages are a way of expressing a portion of 100. So, when we say that 5/6 is 83%, we are saying that 5/6 is equivalent to 83 out of 100. This means that if we were to divide something into 100 equal parts, 83 of those parts would be equivalent to 5/6.

To know more about percentage here.

https://brainly.com/question/13729841

#SPJ4

For a pet shop to approximate 18 rabbits, it would take 6 weeks.

In the question, we have a formula that represents the number of rabbits available with them.

The amount of rabbits is dependent on another variable, Time.

The variables depend on each other, and the number of rabbits with the pet shop relies on the number of weeks.

R(t)= 2t(2/3) + 10

If the number of rabbits is 18, then the value of the equation would be equal to 18.    [R(t) = 18]

18= 2t(2/3) +10

18= 4t/3 + 10

8 X 3 = 4t

24/4 = t

6 = t

Therefore, 18 rabbits are approximated by the pet store in 6 weeks.

For more information regarding linear equations, see:

https://brainly.com/question/30246268

((30$ x4)+40$)-80$=80$

Answer:

6x² + 41x + 48

Step-by-step explanation:

Area (A) = l × w

Therefore,

A = (3x + 16)(2x + 3) (distribute)

A = 6x² + 9x + 32x + 48 (combine like terms)

A = 6x² + 41x + 48

Therefore, the area of the playground is 6x² + 41x + 48.

The required height of the loading dock is approximately 7.746 feet (to the nearest tenth of a foot).

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,
We can use the Pythagorean theorem to solve this problem. Let's call the height of the loading dock "h". The ramp, the distance from the edge of the loading dock to the end of the ramp, and the height of the loading dock form a right triangle. The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the ramp in this case) is equal to the sum of the squares of the other two sides (the height and the distance from the edge of the loading dock to the end of the ramp).

In this case, we can write:

16² = h² + 14²

256 = h² + 196

60 = h²

Taking the square root of both sides, we get:

h = √60

h ≈ 7.746

Therefore, the height of the loading dock is approximately 7.746 feet (to the nearest tenth of a foot).

Learn  more about Pythagorean triplets here:

brainly.com/question/22160915

#SPJ1

Based on the information, the probability that the next buyer did not buy apples last week is: 0.23

To calculate the probability that the next buyer did not buy apples last week we must carry out the following mathematical procedure:

Add up all the values.

Now we add the number of buyers who bought apples

Finally, to find the probability we must divide the number of people who bought apples by the total number of buyers.

However, to find the value of those who did NOT buy apples we must subtract this value from 1.

Learn more about probability at: https://brainly.com/question/30034780

#SPJ1

As per multiplication, the value of 64 times π is 200.96

Multiplication is a fundamental arithmetic operation that involves repeated addition. In this case, we are tasked with finding the result of multiplying 64 and pi. Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is commonly denoted by the Greek letter "π".

To find the product of 64 and pi, we simply need to multiply these two numbers. Multiplication is typically represented using the "×" symbol or the "dot" symbol ( · ). In this case, we can write:

64 × π

Since pi is a mathematical constant, we typically use an approximation of its value in calculations. The commonly used approximation is 3.14, which is accurate to two decimal places. Thus, we can substitute 3.14 for pi and obtain:

64 × 3.14

Using the distributive property of multiplication, we can break down 64 into smaller factors that are easier to multiply with 3.14. For example, we can write:

64 = 60 + 4

Then, we can use the associative property of multiplication to group the factors in a way that makes the calculation easier. For instance, we can write:

64 × 3.14 = (60 × 3.14) + (4 × 3.14)

Now, we can use our knowledge of multiplication tables to calculate the products on the right-hand side. We get:

60 × 3.14 = 188.4

4 × 3.14 = 12.56

Therefore, the final result is:

64 × π = 188.4 + 12.56 = 200.96

To know more about multiplication here.

https://brainly.com/question/5992872

#SPJ4

Answer:

Let's define the variables:

h: the number of hours the driver worked.

d: the number of miles the truck drove.

We know that the driver is paid $16 per hour, so the cost of the driver's labor is:

16h

We also know that the truck incurs an expense of $1.25 per mile driven, so the cost of gas and maintenance is:

1.25d

The total expenses for the driver, gas, and maintenance were $205, so we can set up the following equation:

16h + 1.25d = 205

We also know that the average speed of the truck was 20 miles per hour, so we can set up the following equation:

d = 20h

So the system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove is:

16h + 1.25d = 205

d = 20h

These two equations can be solved simultaneously to find the values of h and d that satisfy both equations.

If the total number of calories is X, then the lowest number is 89, which is 43% of the total, or 206.98 calories. Thus, the response is A.

The middle value of the provided collection of data, when organised in order, is known as the median in statistics. It is possible to arrange the data or observations in either ascending or descending order. For instance, the median of 2,3,4, is 3. The median, a form of average used to determine the center value in mathematics, is another average.

Two easy steps are used to determine the median of a dataset. Put the information provided in ascending order first. The middle data must be chosen next.

To know more about median visit

https://brainly.com/question/28060453

The simplified form of the fraction is 3/u², where u is a positive real number.To simplify this fraction, we can first simplify the denominator by using the exponent rule that says: [tex](a^{m}) ^{n} =(a^{m*n})[/tex]. Applying this rule, we get:

4(u³)⁴ = 4u³*⁴ = 4u¹²

Now, we can substitute this value back into the original fraction and simplify further:

(12u¹⁰)/(4(u³)⁴) = (12u¹⁰)/(4u¹²)

We can simplify the fraction further by dividing both the numerator and the denominator by the greatest common factor (GCF) of 12 and 4, which is 4. Also, we can simplify the exponent by using the exponent rule that says:  [tex]\frac{a^{m} }{a^{n}} =a^{m-n}[/tex]. Applying these steps, we get:

(12u¹⁰)/(4u¹²) = (3u¹⁰)/(u¹²) = 3/u²

Therefore, the simplified form of the fraction is 3/u², where u is a positive real number.

Find more about Fraction

brainly.com/question/29995320

#SPJ4

The value of 135 kg into lbs can be converted by multiplying kilogram by 2.204622  so the answer is 297.624 pounds.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

Pounds = kilograms × 2.20462262184878

= 135 x 2.20462262184878

= 297.624 pounds or lbs.

Learn more about Kilogram into Pounds;

brainly.com/question/30459945

#SPJ4

52 cm is equivalent to nearly 20.47 inches, rounded to two decimal places.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimeters,

Used in the International System of Units,

This is the metric system's present configuration.

52 centimetres equal 20.47 inches (centimeters).

To convert centimeters to inches,

We can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 52 cm to inches,

You can divide 52 by 2.54:

52 cm / 2.54 = 20.47 inches

So, 52 cm is equivalent to nearly 20.47 inches,

rounded to two decimal places.

For similar questions on conversion on inches to cm,

https://brainly.com/question/29750822

#SPJ4

The solution is, pyramid's volume is 96 cm^3.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given information we get,

So we know that the bar edge length is 8 cm (6+2) and the height is 6 cm....

And a pyramid's volume is 1/3 of a prism's volume.

If the base is square and both sides are 6 cm, the area is 36 cm^2.

Then you multiply that area by the height: 288 cm^3.

BUT you have divide that by 3,

because a pyramid's volume is 1/3 of a prism's volume:

288/3= 96 cm^3.

Answer: 96 cm^3

To learn more on volume click :

brainly.com/question/1578538

#SPJ1

We can convert 162 cm to feet by multiplying by the conversion factor to get , 162 cm equivalent to 5.32 feet .

The length or the distance between two points is measured with the help of units such as : meter , centimeter , inches , feet .

We have to convert the length of 162 centimeter to feet ;

We know that , 1 centimeter is approximately equal to 0.0328 feet ;

So , the conversion factor is 0.0328 ;

So , for the conversion  we multiply the given length by 0.0328 ;

On multiplication we get ;

⇒ 162 centimeter = 162 × 0.0328 ;

⇒ 162 centimeter = 5.3136 feet .

Therefore , 162 cm is approximately equal to 5.32 feet .

Learn more about Conversion here

https://brainly.com/question/16814684

#SPJ4

The temperature separating the bottom 91% from the top 9% is given as follows:

P91 = -1.34ºC.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 0, \sigma = 1[/tex]

For the P91, the temperature is obtained as X when Z has a p-value of 0.91, so X when Z = 1.34, hence:

1.34 = X/1

X = 1.34ºC.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

The quadratic equation x2 - 4x + 3 = 0 has two roots. The roots are given by the quadratic formula as x = [4 ± √(16 - 12)]/2, which gives x = [4 ± 2√3]/2. Therefore, the roots are x = 2 ± √3.
The quadratic equation x^2 - 4x - 3 = 0 has two roots.

To find the roots of this equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 1, b = -4, and c = -3. Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-3)))/(2(1))
x = (4 ± √(16 + 12))/2
x = (4 ± √28)/2
x = (4 ± 2√7)/2

Simplifying further, we get:
x = 2 ± √7

Therefore, the two roots of the equation are x = 2 + √7 and x = 2 - √7.

Learn more about quadratic equation here: brainly.com/question/24349828

#SPJ11

The surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.

What is the surface area of the cylinder?

To find the surface area of a cylinder, we need to find the sum of the areas of its curved surface (lateral area) and its two circular bases.

The formula for the lateral area of a cylinder is L = 2πrh, where r is the radius and h is the height. The formula for the area of each circular base is B = πr^2.

We are given that the height of the cylinder is 11 inches and the radius is 8 inches. Therefore, we can calculate:

L = 2πrh = 2 × 3.14 × 8 × 11 = 549.52 in²

B = πr^2 = 3.14 × 8^2 = 200.96 in²

The total surface area is the sum of the lateral area and the two base areas:

Surface area = L + 2B = 549.52 + 2(200.96) = 951.44 in²

Hence, the surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.

To learn more about surface area of the cylinder, Visit

https://brainly.com/question/27440983

#SPJ1

Rory's product is less than Maranda's because 13/9 is less than 13/3

In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.

Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.

A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.

An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.

A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.

Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.

From the table, it appears that Maranda multiplied 4 1/3 by 4 1/3 and then by 1/3, while Rory multiplied 4 1/3 by 1/3 and then by 4 1/3.

Multiplying by 1/3 first reduces the overall size of the number being multiplied, resulting in a smaller product. This is what Rory did, which is why their product is less than Maranda's.

On the other hand, Maranda multiplied by the larger numbers first and then by the smaller fraction, resulting in a larger overall product.

To know more about product visit:

brainly.com/question/29304354

#SPJ1

The complete question is:

Maranda and rory are multiplying 4 1/3 by different fractions the table shows there work

maranda / rory why is rory's product less than maranda's

4 1/3 x 4 1/3 x 1/3

3/3 =4 1/3 1 4/9

The value of the expression is found to be 1 0 when the value of x is equal to 2.

The expression provided to us is 5.x³/x² for x = 2.

Now, in order to evaluate this expression, we will follow the simple,

5.x³/x² = 5x.

First as we can see, x³ can be divided by x²and then we will get x as the outcome of the simple division operation,

So, we will get,

5x

Now, we have to put the value of x equal to 2 so that we get to know about the exact value of the expression,

x = 2,

= 5(2)

= 10

So, the value of the expression is found to be 10 when the value of x was 2.

To know more about mathematical expression, visit,

https://brainly.com/question/1859113

#SPJ4

Complete question - Evaluate the expression 5.x³/x² for x equals to 2.

The lower fence is 56.2428

As the Iq score < lower fence,   Iq score is outlier

What is average/mean?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

data was collected from 221 children

iq scores at age of 7  approximately follow a normal distribution with mean of 87.0 and standard deviation of 11.4.

Let X=iq scores

distribution is

X ~ [tex]N( \mu=87, \sigma=11.4)[/tex]

If one child has iq of 55,

To find outlier, find the lower fence

lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]

[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]

[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]

Using excel function,

[tex]Z_{0.25} = -0.67[/tex]

[tex]Z_{0.75} = 0.67[/tex]

[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]

    =87+(-0.6745)11.4

   = 79.3107

[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]

    = 87+(0.6745)11.4

   = 94.6893

lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]

                    = 79.3107 -1.5(94.6893 - 79.3107 )

                    = 56.2428

So, the  lower fence is 56.2428

As the Iq score <  lower fence,   Iq score is outlier

To learn more about the average/mean from the given link

https://brainly.com/question/1136789

#SPJ1

Answer:

Step-by-step explanation:

The sum of exterior angles of a polygon is 360

Each exterior angle = 360/n

where n is the number of sides

360/12 = 30

Answer is D