The following system of equations are given:
3x+z+y=8
5y-x=-7
3z+2x-2y=15
4x+5y-2z=-3
a. Is it possible to solve for any of the variables using only Equation #1 and Equation #2? Explain your answer. If possible, solve for the variables using only equations #1 and #2.
b. Is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3? Explain your answer. If possible, solve for the variables using only equations #1, #2, and #3.
c. If you found solutions in part b, do these solutions also hold for Equation #4?

The distance of the run is about 7.33 miles.

Let's anticipate that the distance of the run is "d" miles.

We realize that time = distance ÷ velocity.

For the first jogger who averages 8 mph, the time taken to finish the run may be represented as:

t = d ÷ 8

For the second jogger who averages 4 mph, the time taken to complete the same run may be represented as:

t + 35/60 = d ÷ 4

We can simplify this equation by substituting the value of "t" from the first equation:

d ÷ 8 + 35/60 = d ÷ 4

.

Multiplying each aspects through 24 (LCM of 8 and 4), we get:

3D + 7 = 6d

Simplifying this, we get:

d = 7.33 miles (rounded to two decimal locations)

Therefore, the distance of the run is about 7.33 miles.

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Answer:

-4+3n     (if first value corresponds to n=0)

or

-7+3n     (if first value corresponds to n=1)

Step-by-step explanation:

Notice form each term you just need to add 3
For example, the first term is -4, then the second is -4+3=-1

then the third is -4+3+3=2

So you can start from -4 and 3 for each value.

If n=0 is the start value the sequence will be -4+3n

if the first term is n=1  the sequence will be  -4+3(n-1)=-7+3n

So depends if your sequence starts from n=1 or n=0 (which is usually just a convention)

The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.

The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has the following degree, leading coefficient, and constant coefficient:

Degree: The degree of a polynomial is the maximum degree of any term in it.

Here, the term of highest degree is (7x + 3)2 which has a degree of 2.

Therefore, the degree of the polynomial is 2. Leading coefficient: The leading coefficient of a polynomial is the coefficient of the term of highest degree.

Here, the term of highest degree is (7x + 3)2 and it has a coefficient of 49.

Therefore, the leading coefficient of the polynomial is 49. Constant coefficient: The constant coefficient of a polynomial is the coefficient of the term of degree 0.

Here, there is only one such term, which is the constant term 60 (obtained by multiplying the constant terms of each factor: 5 × 4 × 9).

Therefore, the constant coefficient of the polynomial is 60.

Therefore, the polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.

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Step-by-step explanation:

The square root of 22 is an irrational number, which means it cannot be expressed exactly as a finite decimal or a fraction. However, we can approximate it by finding the whole number that is closest to it.

To do this, we can use a calculator or estimation. For example, we can guess that the square root of 22 is between 4 and 5, since 4 squared is 16 and 5 squared is 25. Then we can try averaging these two numbers:

(4 + 5) / 2 = 4.5

This means that 4.5 is an approximate value of the square root of 22. The nearest whole number to 4.5 is 5, so we can say that the whole number nearest to the square root of 22 is 5.

Answer:

5

Step-by-step explanation:

3^2+4^2

9+16=25

sqrt25

The actual outcome of his investment could still be positive or negative, depending on the actual performance of the individual stock.

Since each stock has a 50% chance of being successful and a 50% chance of failing, the expected value of each stock is:

(0.5 * 500) + (0.5 * (-500)) = 0

That is, the expected value of each stock is zero, because the potential gain of $500 is balanced by the potential loss of $500.

Now, since the stocks are independent, the expected value of Ajay's entire investment is simply the sum of the expected values of each individual stock:

Expected value of Ajay's investment = 222 * 0 = 0

So the expected value of Ajay's investment is also zero dollars. This means that, on average, Ajay should not expect to make a profit or a loss from his investment in these 222 stocks. However, the actual outcome of his investment could still be positive or negative, depending on the actual performance of the individual stocks.

Ajay is going to invest his money into 222 different stocks. Both stocks are independent, and each stock has a 50\%50%50, percent chance of being successful and a 50\%50%50, percent chance of failing. Each stock will make Ajay \$500$500dollar sign, 500 if it succeeds or lose him \$500$500dollar sign, 500 if it fails

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The angle measurement between the hands of the clock is 270 degrees. At 9:00, the hour hand points directly to the 9 and the minute hand points directly to the 12.

We know that the hour hand moves 360 degrees in 12 hours (or 30 degrees per hour), and the minute hand moves 360 degrees in 60 minutes (or 6 degrees per minute).

To calculate the angle between the hands, we can use the formula:

angle = |30h - 11m/2|

where h is the hour (9 in this case) and m is the minute (0 in this case). Substituting these values into the formula, we get:

angle = |30(9) - 11(0)/2|

= |270|

= 270

Therefore, the angle between the hands of the clock is 270 degrees.

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The solutions of x1 = 7 and x2 = -3 with x1 through solving the quadratic  equation x²−4x−21=0 by factoring

The equation :x² - 4x - 21 = 0, solve it by factoring it.The first step is to find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3.So, we rewrite the equation using -7 and 3 instead of  -4x:x² - 7x + 3x - 21 = 0.

Group the first two terms and the last two terms: x(x - 7) + 3(x - 7) = 0.

Factor out the common factor of (x - 7): (x - 7)(x + 3) = 0.

Now, we have two factors that when multiplied, give us zero. This means that either (x - 7) = 0 or (x + 3) = 0.

Solving for x, we get: x = 7 or x = -3.

The solutions are x1 = 7 and x2 = -3.The equation x² - 4x - 21 = 0 can be solved by factoring it. To factor this equation, we first find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3. Then we rewrite the equation using -7 and 3 instead of -4x.

The resulting equation is x² - 7x + 3x - 21 = 0.

Next, we group the first two terms and the last two terms to get x(x - 7) + 3(x - 7) = 0.

We factor out the common factor of (x - 7) to get (x - 7)(x + 3) = 0.

We then solve for x to get x = 7 or x = -3. Therefore, the solutions are x1 = 7 and x2 = -3.

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A graph of each inequality is shown in the grid below.

A shape which the solution region represent is a rectangle.

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

0.4r ≤ 120     .....equation 1.

r ≥ 4(360/5)    .....equation 2.

By evaluating the given system of inequalities, we have;

r ≤ 120/0.4

r ≤ 300

r ≥ 4(360/5)

r ≥ 4(72)

r ≥ 288

By combining the system of inequalities, we have:

288 ≤ r ≤ 300

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region between the solid line, and the point of intersection of the lines on the graph representing each.

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The approximate volume of the basketball is 0.00486 cubic meters.

We have,

The formula for the volume of a sphere is:

V = (4/3)πr³

where V is the volume and r is the radius of the sphere.

Converting the radius of the basketball from inches to meters

4.7 inches = 0.11938 meters

Now we can substitute this value for r in the volume formula:

V = (4/3)π(0.11938)³

Using a value of π = 3.14159 and evaluating the expression in the parentheses, we get:

V ≈ 0.00486 cubic meters

Therefore,

The approximate volume of the basketball is 0.00486 cubic meters.

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Thus on the sixth, ninth, twelfth, fifteenth, and eighteenth pages, he reads the same pages.

To tackle proportionality-related mathematical problems, one can apply the unitary method. Finding the value of one unit and then utilising that value to calculate the value of another quantity with a different number of units is what this method entails. Consider the scenario where you are told that an automobile goes 300 miles in 5 hours. The unitary technique can be used as follows to determine how far the car drives in 8 hours: Calculate what an hour is worth: 1 hour is equal to 300/5, or 60 miles. 5 hours equals 1 unit. Use this number to calculate the value of eight hours: 8 hours equals 8/1 units, hence 8 x 60 = 480 miles are covered during that time.

given

Each of them reads roughly one-third of the story's pages when the three of them are reading it together.

As a result, Beth reads the first, fourth, seventh, and cdots pages, Carolyn reads the second, fifth, and eighth, and cdots pages, and George reads the third, sixth, and ninth.

When just Carolyn and George are reading the narrative, Carolyn reads the first page and George reads the second, and so on through the remaining pages.

Thus on the sixth, ninth, twelfth, fifteenth, and eighteenth pages, he reads the same pages.

So, $3+5=8 ($boxed) is the amount of pages that Carolyn and George read that are equal to the amount of pages they would have read if Beth had been present.

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Therefore , the solution of the given problem of volume comes out to be the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Cubic measurements are denoted by the characters cm3 and in3. To determine an item's size, you could use its bulk, though. The object's weight is typically transformed into mass units like grammes and kilos.

Here,

The formula for a cylinder's capacity can be used to calculate the height:

=> V = πr^2h

where the volume is V, the radius is r, and the height is h.

Inputting the numbers provided yields:

=> 1 1/16 = π(1/4)^2h

Simplifying:

=> 1.0625 = π(1/16)h

=> 1.0625 = (π/16)h

Adding 16/ to both sides:

=> h = (16/π) x 1.0625

=> h = 16.8125/π

=> h ≈ 5.3529

=> H = 5.353 inches is the result of rounding to the closest thousandth.

As a result, the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.

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if it has a diameter of 10, that means its radius is half that or 5.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=18 \end{cases}\implies V=\pi (5)^2(18)\implies V\approx 1413.72~in^3[/tex]

The expression that represents the cost after the 11% discount is 0.89c. This means that Boubacar will pay 89% of the original cost after the discount has been applied.

To calculate the discount, you need to determine the discount rate, which is usually a percentage of the original price. Multiply the discount rate by the original price to find the amount of the discount.

Finally, subtract the discount amount from the original price to get the discounted price.

The discount that Boubacar gets on his purchase is 11% of the total cost before tax and discount. To calculate the discount, we multiply the total cost (c) by 11% or 0.11, which gives us:

Discount = 0.11c

To find the cost after the discount, we subtract the discount from the total cost. This gives us:

Cost after discount = c - Discount

Cost after discount = c - 0.11c

Cost after discount = 0.89c

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The value of tan α is  [tex]\frac{3}{4}[/tex] . This value has been obtained by using the concept of trigonometry.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of right-angle triangles, which even includes their sides, angles, and relationships.

We know that the value of tan α is the ratio of a triangle's base to the triangle's perpendicular.

In the question, we are given that the base is 15 and the perpendicular is 20.

So, from the above information, we get the value as

⇒tan α = [tex]\frac{15}{20}[/tex]

⇒tan α = [tex]\frac{3}{4}[/tex]

Hence, the value of tan α is  [tex]\frac{3}{4}[/tex] .

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There will be 23 highway signs on the road trip, including one at the end of the road trip.

The total length of the road trip is 13.8 hours. To solve for the number of highway signs on the road trip, we need to use the formula for finding out how many times a certain number can fit into another number. This formula is N = A/B, where N is the number of times B can fit into A. In this case, B is the time between highway signs (0.6 hours) and A is the total length of the road trip (13.8 hours). Plugging these values into the formula, we get N = 13.8/0.6 = 23. So, there will be 23 highway signs on the road trip, including one at the end of the road trip.

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Answer:

Yes, they do

Step-by-step explanation:

The more you focus on a concept, the more you get an understanding of it without being taught by another person.

Hard math concepts are hard cause you haven't found an easier way to get an understanding of it.

The given data shows that in 2000, the population of a country was approximately 6.19 million, and by 2050, it is projected to grow to 10 million. The exponential growth model can be represented as:

A = A0e^{kt}

Where A0 = 6.19 (initial population in 2000), A = 10 (projected population in 2050), T = 50 - 00 = 50 years (time period between 2000 and 2050).

Substituting the values in the formula, we get:

10 = 6.19 e^{k × 50}

Solving for k:

e^{k × 50} = 10/6.19

k × 50 = ln(10/6.19)

k = ln(10/6.19) / 50

k = 0.0169

Therefore, the population of the country will be given by A = 6.19 e^{0.0169t} where t represents the time in years after 2000.

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The expression for the amount of change Zina should receive would then be 20 - (0.30 x 10) = 17.00. This means that Zina should receive 17.00 in change from the clerk.

What is amount?

Amount is the quantity or amount of something that is available, measurable, or given. It is a numerical value. Amount can refer to a quantity of money, goods, or services that is owed, requested, or given. It can also refer to the total cost of items or services. Amounts can be measured in both the physical and digital world. Amount is used in accounting, finance, and other fields to measure and keep track of assets and liabilities.

The expression that represents the amount of change Zina should receive is 20 - (0.30p). This expression takes the original amount of money given to the clerk, twenty dollars, and subtracts out the total cost of the bananas, which is 0.30p. The 'p' in this expression represents the number of pounds of bananas Zina purchased.

To determine the amount of change Zina should receive, the clerk must first calculate the total cost of the bananas. This is done by multiplying the number of pounds of bananas purchased by the cost per pound. Once the total cost of the bananas is calculated, it is then subtracted from the twenty dollars given. The resulting number is the amount of change Zina should receive.

For example, if Zina purchased 10 pounds of bananas at 30 cents per pound, the total cost of the bananas would be 10 x 0.30 = 3.00. The expression for the amount of change Zina should receive would then be 20 - (0.30 x 10) = 17.00. This means that Zina should receive 17.00 in change from the clerk.

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Answer:

To ensure that you have grabbed 250 balls of one color, you need to use the Pigeonhole Principle. The worst-case scenario is that you grab 249 balls of each color, totaling 996 balls. Therefore, the smallest amount of balls you need to grab is 997, which guarantees that you have grabbed 250 balls of one color.

To explain further, let's consider the worst-case scenario where you grab 249 red balls, 249 green balls, 249 blue balls, and 249 yellow balls. This totals to 996 balls. However, if you grab just one more ball, you will have a total of 997 balls, and since there are only four colors, at least one color will have 250 balls or more. Therefore, by grabbing 997 balls, you can be sure that you have grabbed at least 250 balls of one color.

Answer:

997

Step-by-step explanation:

I multiplied 249 by 4 first. This is because I wanted to find how many balls the person could grab in total without having 250 of the same color.

249*4= 996

However, the question wants to guarantee that one color has 250.

So I did 996+1=997. (which means there could be: 249 red, 249 yellow, 249 green, and 250 blue)

This means that every other color could be at 249, but one would guarantee to be at 250 with 997 pulls

About 16 people among the 1,000 insured people can file a claim for a surgical procedure.

Profit is the financial gain earned by a business or an individual after deducting all the expenses and costs associated with generating that revenue. It represents the difference between the total revenue earned and the total expenses incurred.

The total amount collected in premiums over 3 years for Bracken is:

$100 x 1,000 x 3 = $300,000

Assuming x people among the 1,000 insured people file a claim for a surgical procedure, the total amount paid out in claims by Bracken would be:

$25,000 x x = $25,000x

The total deductible paid by the claimants would be:

$3,500 x x = $3,500x

So, the total amount paid out by Bracken would be:

$25,000x + $3,500x = $28,500x

For Bracken to break even, the total amount collected in premiums should be equal to the total amount paid out in claims plus the deductible for 3 years.

$300,000 = $28,500x + $3,500(1,000 - x)

Simplifying and solving for x, we get:

x = 16

Therefore, about 16 people among the 1,000 insured people can file a claim for a surgical procedure for Bracken to break even over the passage of 3 years.

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The complete question is:

Atrap and Bracken are two rival insurance companies. Atrap and Bracken have premiums of $150 and $100 and deductibles of $2,500 and $3,500 respectively. The average expense of surgery is $25,000. For Bracken to break even (suffer no loss and earn no profit) over the passage of 3 years, about how many people among the 1,000 insured people can file a claim for a surgical procedure?

a -10

b- 14

c- 16

d- 17

e- 20

The area will rise by a factor of four if we double the base and height of a trapezoid.

A quadrilateral with a single set of parallel sides is referred to as a trapezoid. The parallel and non-parallel sides are referred to as bases and legs, respectively. The distance between the bases of a trapezoid measured perpendicularly is its height.

The formula for a trapezoid's area is:

Area is equal to (base1+base2)*height / 2.

Considering that the height is 6 millimeters, the first base is 5 millimeters, and the secondary base is 7 millimeters, we may determine the trapezoid's initial area as follows:

Area = 1/2 *(5 + 7)* 6 = 36 sq. mm

Doubling the height and both bases:

New base 1 = 2 * 5 = 10 mm

New base 2 = 2 * 7 = 14 mm

New height = 2 * 6 = 12 mm

The new area of such trapezoid can be calculated using the same formula:

New Area = 1/2* (10 + 14) * 12 = 144 sq. mm

When we compare the new area to the old area, we are able to see that the new area has been four times bigger.

So, if the base and height of just a trapezoid are both doubled, the area will grow by a factor four.

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The equation of the line that is perpendicular to the equation is y = -1/5x

The given line has a slope of 5, which means that any line perpendicular to it will have a slope that is the negative reciprocal of 5. The negative reciprocal of 5 is -1/5.

Let m be the slope of the line perpendicular to y = 5x - 2. Then, the equation of this line can be written in point-slope form as:

y - y1 = m(x - x1)

where (x1, y1) is the point where the line passes through, which is the origin in this case. So, we have:

y - 0 = (-1/5)(x - 0)

Simplifying this equation, we get:

y = (-1/5)x

Therefore, the line perpendicular to y = 5x - 2 and passing through the origin has a slope of -1/5 and a y-intercept of 0. Its equation is y = (-1/5)x.

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It will take 55 days to finish the renovation with 25 men.

If 34 men can finish the renovation in 40 days, we can say that the number of men is inversely proportional to the number of days needed to finish the work. Therefore, we can write:

Number of men × Number of days = Constant

We can find the value of the constant by using the given information:

34 men × 40 days = 1360

This means that the constant is equal to 1360.

If 9 men withdraw before the work started, then the number of men who will work on the renovation is 34 - 9 = 25.

We can now use the constant to find the number of days needed to finish the renovation with 25 men:

25 men × Number of days = 1360

Number of days = 1360 ÷ 25

Number of days = 54.4

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The statement "using higher order functions, complete the mul by num function. this function should take an argument and return a one argument function that multiplies any value passed to it by the original number" is True. It is possible to complete the `mul_by_num` function using higher order functions. A higher order function is a function that either takes one or more functions as arguments, or returns a function as its result.

In this case, the `mul_by_num` function should take an argument and return a one argument function that multiplies any value passed to it by the original number. Here's how you can do it:

```python
def mul_by_num(num):
   def num_function(val):
       return val * num
   return num_function
```

The `mul_by_num` function takes an argument `num` and returns a one argument function `num_function` that multiplies any value passed to it by the original number `num`. The `num_function` is a higher order function because it is returned by the `mul_by_num` function.

You can use the `mul_by_num` function like this:
```python
mul_by_5 = mul_by_num(5)
print(mul_by_5(10)) # 50
```

The `mul_by_num` function is called with the argument `5` and returns a one argument function `mul_by_5` that multiplies any value passed to it by 5. When the `mul_by_5` function is called with the argument `10`, it returns the result `50`.

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Answer:

72

Step-by-step explanation:

The measure of the inscribed angle(DEF) is half the measure of its intercepted arc (Arc FD)

The measure of are FD is 144 and half of that is 72.

So the measure of angle DEF is 72 degrees.

Answer:

72°

Step-by-step explanation:

∠DEF is an inscribed angle equal to half the arc on which it rests

∠DEF = 0,5 × 144 = 72°

Answer:

Q1: no idea

Q2: 2 kids get 2 pieces of taffy and 1 piece of licorice and the other three get 2 pieces of licorice and 1 piece of taffy.

Step-by-step explanation:

question 2 is quite obvious but no one can get the same amount of everything so the answer that i gave makes the most sense.

Answer:

5 days .......

Step-by-step explanation:

Stefan has 4½ cups of oat

He uses 3¼ to make granola

What he has left 4½-3¼ = 1¼

If he feeds ¼of a cup to parrots a day, then he has 5 days feed from 1¼

Calculation 1¼ ÷ ¼

Change to improper fraction

5/4 ÷ 1/4 = 5/4 x 4/1

Ans 20/4 = 5days

As per the given percentage, the original price to be $180.00.

Let's begin by defining what percentage means. A percentage is a fraction that represents a portion of a whole expressed as a fraction of 100. For example, 25% can be written as 25/100 or 0.25 as a decimal.

Now, let's apply this concept to the problem. We know that the original price increased by 25%, which means the new price is 125% of the original price. We can represent this mathematically as:

New price = Original price + 25% of the original price

125% of the original price = Original price + 25% of the original price

1.25 x Original price = Original price + 0.25 x Original price

1.25 x Original price = 1.25 x Original price

Original price = (225.00 / 1.25)

Therefore, the original price was $180.00.

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