Solve the following system of equations:
2x + 3y − z = 1
3x + y + 2z = 12
x + 2y − 3z = −5
PLEASE HELP!! 25 POINTS!!

Part A: A

Part B: Julia collected 18.65, Keller collected 61.15, and Israel collected 45.15

Answer:

[tex]\frac{2 \sqrt{5}}{5}[/tex]

Step-by-step explanation:

As given by SOH-CAH-TOA

tan is equal to opposite/adjacent.

therefore for A, the opposite would be equal to 2, and adjacent would be equal to [tex]\sqrt{5}[/tex] as the hypotenuse is never referred to as an adjacent side. so the answer would be tan(A) = [tex]\frac{2}{\sqrt{5}}[/tex] however, to rationalize the denominator you must multiply the fraction by [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] .

[tex]\frac{2}{\sqrt{5}} *\frac{\sqrt{5}}{\sqrt{5}} = \frac{2 * \sqrt{5}}{\sqrt{5} *\sqrt{5}}[/tex]

then simplify

[tex]\frac{2 \sqrt{5}}{5}[/tex]

f(275) represents the average number of days houses stay on the market before being sold for $275,000.

From the question, we have the following parameters that can be used in our computation:

f(p) is the average number of days a house stays on the market before being sold for price p in $1,000s

This means that

In f(275), we have

p = 275

So, the meaning is:

f(275) is the average number of days a house stays on the market before being sold for price $275,000s

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The distribution of snowfall amounts is best described as bimodal, with modes at 2 inches and 7 inches. So, the range is a more appropriate measure of variation than the standard deviation.

A bimodal distribution can be identified in a histogram when two distinct groups can be seen there. A bimodal distribution actually has two modes or two different data clusters.

In a bimodal distribution, no particular data value has the highest frequency of occurrence, rather two data values have the highest frequency.

The line plot of the distribution by Damon has two modes and is, therefore, bimodal.

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The description describes the solutions to this inequality in all the positive numbers that are greater than ten. The correct option is B.

Relationships between two expressions that aren't equal to one another are known as inequalities. Social justice theories are fundamentally based on the idea of inequality, which is the condition of not being equal, especially in terms of status, rights, and opportunities.

The given equation is 9 > 52.

everything that is positive and bigger than 10

Therefore, the correct option is B. All the positive numbers are greater than ten.

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Answer:

D. A = s × s

Step-by-step explanation:

D. A = s × s is an area formula. Area is side times side. This is an area formula for a square. The units of area are square units. Since Jennifer has square inches in her answer, she was working on an area problem.

A. and C. are perimeter formulas. Perimeter is the distance around the outside of a shape. The units of perimeter are straight up plain, one-dimensional units like inches (or feet, meters, miles, km)

B. is a volume formula. The units of volume is cubic units or units to the third power.

The answer is D.

Answer:

it would be 3 or 2

Step-by-step explanation:

Answer: To answer this question, we need to calculate the maximum possible speed of the train based on the given information and check if it is greater than 160 km/h.

First, let's use the given information to find the range of possible speeds of the train. The time taken by the train is given as 110 minutes, correct to the nearest 5 minutes. This means that the actual time taken by the train could be anywhere between 107.5 minutes and 112.5 minutes.

Converting the time to hours, we get:

Lower bound of time = 107.5 minutes = 107.5/60 hours = 1.792 hours

Upper bound of time = 112.5 minutes = 112.5/60 hours = 1.875 hours

Now, let's use the given distance of 270 km, correct to the nearest 10 km, to find the range of possible average speeds of the train. The lower bound of the distance is 265 km, and the upper bound is 275 km.

Lower bound of speed = 265 km / 1.875 hours = 141.3 km/h

Upper bound of speed = 275 km / 1.792 hours = 153.5 km/h

Therefore, based on the given information, the maximum possible speed of the train is 153.5 km/h, which is less than 160 km/h.

So, we can conclude that the average speed of the train could not have been greater than 160 km/h.

Step-by-step explanation:

The calculated value of sec^-1(1.4) is 44.41 degrees

The inverse secant function, denoted as sec^-1(x), returns the angle whose secant is x.

In other words, if secθ = x, then sec^-1(x) = θ.

To find the value of sec^-1(1.4), we need to find the angle whose secant is 1.4.

However, we know that the range of the secant function is [-∞, -1] ∪ [1, ∞], which means that sec^-1(x) is only defined for values of x that fall within this range.

Uisng a graphint tool, we have

sec^-1(1.4) = 44.41

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Answer: 228[tex]cm^2[/tex]

Step-by-step explanation:

The lateral area is 2lh + 2wh

= (2 * 14 * 6) + (2 * 5 * 6)

= 228[tex]cm^2[/tex]

Answer:

Let s be the number of smartphones.

81 = .45s, so s = 180

Answer:

36.45

Step-by-step explanation:

You make 45 into a percentage, which is 0.45%. Then, multiply 0.45 by 81 and you get 36.45. Hope this helps! And if you’re incorrect I deeply apologize. I tried my best and I’m 95% sure that I’m correct.

The maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.

The Federal Unemployment Tax Act (FUTA) tax rate is 6% on the first $7,000 paid to each employee in a calendar year. Therefore, the maximum FUTA deduction for each employee is $420 ($7,000 x 0.06).

Person 1 earned $4700, so the FUTA deduction for Person 1 is $282 ($4700 x 0.06).

Person 2 earned $19,800, but only the first $7,000 is subject to FUTA. Therefore, the FUTA deduction for Person 2 is $420.

Person 3 earned $6500, so the FUTA deduction for Person 3 is $390 ($6500 x 0.06).

The total FUTA deduction for the first quarter is the sum of the FUTA deductions for each employee:

$282 + $420 + $390 = $1092

Therefore, the maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.

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The balance in the account after the given period is [tex]\$6,872.74[/tex]  

we know that

The compound interest formula is equal to  

[tex]\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}[/tex]

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]\text{t}= 8 \ \text{years}[/tex]

[tex]\text{P}=\$4,000[/tex]

[tex]\text{r}=0.07[/tex]

[tex]\text{n}=1[/tex]

substitute in the formula above

[tex]\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74[/tex]  

Answer:

[tex]9 {x}^{2} + 3 {x}^{3} [/tex]

[tex]3 {x}^{2} (3 + x)[/tex]

[tex]3 {x}^{2} (x + 3)[/tex]

Answer:

A) 150%

B) 20.67 J

Step-by-step explanation:

A) To determine the efficiency of the engine, we can use the formula:

efficiency = (work output / heat input) x 100%

In this case, the engine does 62 J of work each cycle, so the work output is 62 J. We're also given that the engine absorbs 2 times as much heat as it discharges to the environment, so we can express the heat input as 2 times the heat discharged:

heat input = 2 x heat discharged

Therefore, we can rewrite the efficiency formula as:

efficiency = (62 J / (2 x heat discharged)) x 100%

Simplifying this expression, we get:

efficiency = 31 J / heat discharged

Now we need to determine the value of heat discharged. We know that the engine absorbs 2 times as much heat as it discharges, so the net heat input is 3 times the heat discharged:

net heat input = heat input - heat discharged = 2 x heat discharged - heat discharged = heat discharged

Therefore, we can express the net heat input as:

net heat input = 3 x heat discharged

Now we can use the first law of thermodynamics, which states that the net heat input is equal to the work output plus the heat discharged:

net heat input = work output + heat discharged

Substituting the given values, we get:

3 x heat discharged = 62 J + heat discharged

Solving for heat discharged, we get:

heat discharged = 20.67 J

Now we can calculate the efficiency:

efficiency = 31 J / 20.67 J = 1.50 or 150%

Therefore, the efficiency of the engine is 150%.

B) To determine the quantity of heat discharged to the environment each cycle in Joules, we can use the value we calculated above for heat discharged:

heat discharged = 20.67 J

Therefore, the quantity of heat discharged to the environment each cycle is 20.67 J.

Hope this helps!

f(4) = 537. and f(-3) = 363.  To find f(-3), we replace x with -3 in the expression similarly for x=4.

what is expression  ?

In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.

In the given question,

To find f(-3), we replace x with -3 in the expression:

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

= 3(81) - 4(-27) + 3(9) + 15 - 3

= 243 + 108 + 15 - 3

= 363

Therefore, f(-3) = 363.

To find f(4), we replace x with 4 in the expression:

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

= 3(256) - 4(64) + 3(16) - 20 - 3

= 768 - 256 + 48 - 23

= 537

Therefore, f(4) = 537.

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Therefore , the solution of the given problem of unitary method comes out to be Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

Use the tried-and-true fundamental methodology, the real variables, and any useful information you learn from the general and specific questions to complete the assignment. Customers may be given another chance to taste the products in expression response. If these improvements don't happen, we'll lose out on significant advancements in programming comprehension.

Here,

Due to the idea of unit pricing, Stacy's Bake Shop sells cupcakes for less money than The Best Cake Shop.

In order to compare products with varying quantities or sizes, unit pricing, also known as price per unit, is used.

In this instance, Stacy's Bake Shop charges $21 for a dozen cupcakes, hence the price per cupcake is calculated as

=>  $21 /12, or $1.75 per cupcake.

On the other hand, The Best Cake Shop charges $12 for a half-dozen cupcakes; this indicates that each cupcake costs $2, or $12 divided by six.

As a result, Stacy's Bake Shop charges $1.75 less each cupcake than The Best Cake Shop, which charges $2.

As a result, Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

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The  area of triangle ABC is 6cm²

A triangle is a three-sided polygon that consists of three edges and three vertices.  It is also known as the trigon and has special names such as the hypotenuse (opposite the right angle) and legs (the other two sides). It can also refer to a percussion instrument consisting of a rod of steel bent into the form of a triangle open at one angle.

The area of the triangle is given as

Area= 1/2absinC

But the CosB = Adj/Hypo

Cos60 = Adj/12

1/2 = Adj/12

corss and multiply to have

2A = 12

Therefore Adj = 6

Therefore base = 6*2 = 12

Applying the formula we have Area= 1/2acsinB

Area = 1/2* 12*12*Cos60

Area = 12*1/2 =6cm²

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The estimated actual temperature (x) when the temperature adjusted for wind chill (y) is -35 degrees Fahrenheit =

approximately -6.92 degrees Fahrenheit.

To estimate the actual temperature (x) when the temperature adjusted for wind chill (y) is given as -35 degrees Fahrenheit using the formula y = -26 + 1.3x, we can substitute y with -35 and solve for x.

-35 = -26 + 1.3x

Adding 26 to both sides to isolate the x term:

-35 + 26 = 1.3x

-9 = 1.3x

Dividing both sides by 1.3 to solve for x:

x = -9 / 1.3

x ≈ -6.92

Thus, the estimated actual temperature (x) when the temperature adjusted for wind chill (y) is -35 degrees Fahrenheit would be approximately -6.92 degrees Fahrenheit.

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The estimated actual temperature is -6.92 degrees Fahrenheit.

We can use the given formula to solve for x when y is known. Rearranging the formula, we get:

x = (y + 26) / 1.3

Substituting y = -35 into this formula, we get:

x = (-35 + 26) / 1.3

x = -6.92 (rounded to two decimal places)

Therefore, the estimated actual temperature is -6.92 degrees Fahrenheit.

The term actual temperature typically refers to the true or measured temperature of an object, substance, or environment. It is the temperature that is currently present in a given location or situation, as opposed to a predicted or estimated temperature. The actual temperature can be measured using a thermometer or other temperature sensing device.

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Answer:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where A is the future value, P is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.

(a) To find the present value of the money, we need to solve for P in the formula above. We are given that A = $3000 and t = 18/12 = 1.5 years. The interest rate is 6% per year, compounded monthly, which means n = 12. Substituting these values into the formula, we get:

3000 = P(1 + 0.06/12)^(12*1.5)

Simplifying and solving for P, we get:

P = 3000 / (1 + 0.06/12)^(12*1.5)

P = $2,572.39

Therefore, the equivalent value of the money now is $2,572.39.

(b) To find the equivalent value of the money one year from now, we need to calculate the future value of $1 after one year, and then multiply it by the present value we found in part (a). The future value of $1 after one year, at 6% per year, compounded monthly, is:

FV = 1*(1 + 0.06/12)^(12*1)

FV = $1.06168

Multiplying this by the present value we found in part (a), we get:

$2,572.39 * $1.06168 = $2,735.92

Therefore, the equivalent value of the money one year from now is $2,735.92.

(c) To find the equivalent value of the money three years from now, we need to calculate the future value of $1 after three years, and then multiply it by the present value we found in part (a). The future value of $1 after three years, at 6% per year, compounded monthly, is:

FV = 1*(1 + 0.06/12)^(12*3)

FV = $1.19102

Multiplying this by the present value we found in part (a), we get:

$2,572.39 * $1.19102 = $3,066.63

Therefore, the equivalent value of the money three years from now is $3,066.63.

The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points .

A circle is a closed shape made up of all elements in a plane that are indistinguishable from a predetermined point known as the centre. The radius (r) of a circle is the separation between the circle's centre and any other point on the circumference.

given

These procedures can be used to graph the circle :

Determine the circle's centre. The point in this instance serves as the centre (5, 6).

Determine the circle's radius. The circle's diameter is 4/2, or two.

Place the circle's centre on the coordinate plane.

Plot points that are 2 units distant from the centre in all directions to form the circle.

The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points, and the points (5, 4) and (5, 8) are two points on the circle's y-axis.

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The given graph's Euler path is represented as a series of vertices visited in the following order: EBADCFEACBE.

A path in a finite graph known as an Euler path is one that traverses each edge precisely once while yet allowing for the revisiting of vertices.

A similar Euler trace that begins and finishes at the same vertex is known as an Euler circuit or cycle. When Leonhard Euler found a solution to the Seven Bridges of Konigsberg puzzle in 1736, it was first brought up for discussion.

A path known as an Euler path is one that utilises every edge in the graph once and only once. It doesn't have to return to the starting point because it is a path. A circuit that utilises every edge in the diagram once is known as an Euler circuit. As it is a circle, it should start and terminate at the same vertex.

If a graph has no more than two vertices of odd degree, it has an Euler path.

If every vertex has an even degree, the graph has an Euler circuit.

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Using the simple interest formula, Whitney earned an interest of $26,000 in 4 years.

The simple interest system does not charge interest on accumulated interest (unlike the compound interest system) but only on the principal for each period.

The formula for computing the simple interest amount for the period is given as I = PRT, where I is the interest earned, P is the principal (starting amount), R is the interest rate expressed as a decimal, and T is the time in years.

Principal = $50,000

Simple interest rate = 13%

Investment period = 4 years

Simple interest earned = $26,000 ($50,000 x 13% x 4)

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Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

[tex]\frac{x}{10}[/tex] = [tex]\frac{14}{4}[/tex] = [tex]\frac{7}{2}[/tex] ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

The number of different passwords, considering 2 digits and 2 letters, is given as follows:

A. 6,760,000.

B. 3,276,000.

The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The password is composed by:

With repetition, we have that:

Hence the number of passwords is given as follows:

10^4 x 26² = 6,760,000.

Without repetition, we have that:

Hence the number of passwords is given as follows:

10 x 9 x 8 x 7 x 26 x 25 = 3,276,000.

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Answer: 12

Step-by-step explanation: distribute 5 to 20 and -m which gives you

100 - 5m = 40. Subtract 100 on both sides which gives you -5m = -60. Divide both sides by -5 which gives you m = 12

Answer:

Step-by-step explanation:

Answer: Pete is twice as old as Chris.p = 2c  Seven years ago the sum of their ages were 31.(p-7) + (c-7) = 31p + c - 14 = 31p + c = 31 + 14p + c = 45Find their ages now replace p with 2c2c + c = 453c = 45c = 45/3c = 15 is Chris's agethenp = 2(15)p = 30 is Pete's age::Check solutions in the statement"Seven years ago the sum of their ages were 31"30-7 + 15-7 = 31

Answer: B

Step-by-step explanation:

The word that would indicate that the cat was afraid of the veterinarian is "cowered." "Cowered" means to crouch down in fear or shame. So, the sentence would be: "The cat cowered under the table when the veterinarian came into the examining room."

Answer:

The lateral area of a cone is given by the formula:

L = πrs

Where r is the radius of the base, s is the slant height, and π is pi.

We are given that the lateral area L is 587π cm^2 and the radius r is 32 cm. Substituting these values into the formula, we get:

587π = π(32)s

Simplifying, we can cancel the π on both sides of the equation:

587 = 32s

Dividing both sides by 32, we get:

s = 18.34375

Rounding to the nearest tenth, we get:

s ≈ 18.3 cm

Therefore, the slant height is approximately 18.3 cm.

Step-by-step explanation: