what extraneous solution arises when solving for the point of intersection of the line f(x)=-1/2x+6 and the square root function f(x)= √x-4

Answer:

If x = 3 and y = 2.3^3, then we can evaluate y using exponents:

y = 2.3^3 = 2.3 × 2.3 × 2.3 = 12.167

So, y = 12.167 when x = 3.

Next, if we want to solve the equation y = 2[?] using order of operations, we need to evaluate what is inside the brackets first. We know that y = 12.167, so we can substitute that value into the equation:

y = 2[?]

12.167 = 2[?]

To solve for the missing value inside the brackets, we need to divide both sides by 2:

12.167 ÷ 2 = ?

6.0835 = ?

Therefore, the solution is y = 2(6.0835), or y = 12.167, which we already found earlier.

To calculate your fuel consumption in gallons per hour, divide the speed (in miles per hour) by the fuel efficiency (in miles per gallon). This will give you the gallons per hour (GPH).

For example, if your speed is 50 mph and your fuel efficiency is 30 mpg, your fuel consumption would be 1.67 GPH (50/30). You can then use this result to estimate your fuel costs and overall fuel consumption over a certain period of time.

To understand this concept better, it is important to know that speed (in mph) and fuel efficiency (in mpg) are inversely related. This means that as your speed increases, your fuel efficiency decreases, and as your speed decreases, your fuel efficiency increases.

So, if you want to maximize your fuel efficiency, you need to drive at the lowest possible speed. Additionally, the higher the fuel efficiency, the lower the fuel consumption in GPH.

In short, you can use the readout from your odometer and fuel efficiency meter to calculate your fuel consumption in GPH by dividing the speed (in mph) by the fuel efficiency (in mpg). This result can help you estimate your fuel costs and overall fuel consumption.

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The characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

In a polynomial expression, a coefficient is the numerical factor that is multiplied by a variable or variables raised to a certain power. In the expression 5.1xy - 4x + y - 1.5, the coefficient 5.1 is multiplied by the variables x and y, raised to the first power. Therefore, the term 5.1xy consists of the coefficient 5.1 and the variables x and y.

In contrast, the other terms in the polynomial do not have a coefficient that contains a decimal or a fraction. The term -4x has a coefficient of -4, the term y has a coefficient of 1, and the constant term -1.5 has a coefficient of -1.5.

Thus, the characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

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The area of the trapezoid is 70 square centimeters.

locating a right trapezoid's area. A = (a + b) x h/2 is the formula to calculate the area of a right trapezoid.

We must apply the following calculation to determine the area of the trapezoid:

A = (b1 + b2) * h/2

where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides (or the distance between the parallel sides).

We can observe that in this instance, b1 = 12 cm, b2 = 8 cm, and h = 7 cm. When we plug these numbers into the formula, we get:

A is equal to (12 + 8) x 7 cm / 2.

A = 20 cm * 7 cm / 2

A = 70 cm²

Hence, the trapezoid has a surface area of 70 square centimetres.

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To achieve the maximum output from his electrical system, Steve should set the input to 6, the x-coordinate of the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex].

To find the input that will result in the maximum output of the electrical system, we need to find the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola is the point where the curve reaches its highest or lowest point, depending on whether the parabola opens upward or downward. In this case, the coefficient of [tex]x^2[/tex] is negative, which means the parabola opens downward, and the vertex represents the maximum point.

We need to find the vertex of the parabola given by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola with equation [tex]y = ax^2 + bx + c[/tex] is given by the formula x = -b/2a.

In this case, a = -1, b = 12, and c = -20, so the x-coordinate of the vertex is:

x = -b/2a = -12/(2*(-1)) = 6

Therefore, the input at which Steve will reach his maximum output is x = 6.

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The experimental (empirical) probability that the next child is a boy given that a family has five children: 3 boys and 2 girls is 0.6.

Given that the family has five children, 3 of whom are boys and 2 are girls. If we want to know the experimental probability that the next child is a boy, we need to find the ratio of the number of boys to the total number of children. Since the family has three boys and two girls, the total number of children is:
Total number of children = 3 + 2 = 5
Therefore, the probability of the next child being a boy is given by the ratio of the number of boys to the total number of children.
P(B) = Number of boys/Total number of children
P(B) = 3/5P(B) = 0.6
Therefore, the experimental (empirical) probability that the next child is a boy is 0.6.

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The probability of winning the New York State Numbers Lottery is 1 in 1000.

When you pay for a ticket, you pick a number between 000 and 999. If your number is drawn, you win $500, meaning you made a profit of $490. If you don't win, you will lose the $1 that you paid for the ticket.

To calculate the probability of winning the New York State Numbers Lottery, you must first consider the total number of possible outcomes. Since you can pick a number between 000 and 999, there are 1000 possible outcomes. This means that your chance of winning is 1 in 1000, or 0.1%.

It is important to remember that the New York State Numbers Lottery is a game of chance, meaning that there is no guarantee of winning.

However, if your number is drawn, you can win up to $500, which is a profit of $490. The odds of winning are 1 in 1000, and if you lose, you will only lose the amount you paid for the ticket.

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The percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

Percent error is a measure of the difference between an actual value and an estimated or measured value, expressed as a percentage of the actual value. It is used to evaluate the accuracy of measurements or calculations.

To calculate the percent error for Jason's measurement, we first need to find the absolute error, which is the difference between his measurement and the actual value:

Actual value minus measured value equals absolute error.

Absolute error = |14 - 13|

Absolute error = 1 inch

Next, we can use the formula for percent error:

(Absolute error / Actual Value) x 100% equals the percent of error.

Percent error = (1 / 14) x 100%

Percent error = 0.0714 x 100%

Percent error = 7.14%

Therefore, the percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

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Answer:

I believe the answer would be 30 people.

Step-by-step explanation:

To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.

The function f(x) = 3x - 5 has the defined set of range and domain of the function.

The range {−11,−5,1,7,13} and the domain {−2,0,2,4,6} of the function

Taking the first function;

f(x) = 3x - 5

When x = -2, f(x) = 3(-2) - 5 = -11

When x = 0, f(x) = 3(0) - 5 = -5

When x = 2, f(x) = 3(2) - 5 = 1

When x = 4, f(x) = 3(4) - 5 = 7

When x = 6, f(x) = 3(6) - 5 = 13

Therefore, the function f(x) = 3x - 5 produces the given range when the domain is {−2,0,2,4,6}.

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complete question :

Which function produces a range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6}

f(x) = 3x − 5

f(x) = −3x + 4

f(x) = x + 2

f(x) = −5x + 3

The volume of the cylinder with radius 19 yd and height 21 yd is 23,804.34 cubic yard

Volume refers to the unit of three-dimensional measure of space that comprises a length, a width and a height. It is measured in units of cubic centimeters in metric, cubic inches or cubic feet.

Volume of a cylinder = π × r ²× h

Where,

π = 3.14

Radius, r = 19 yd

Height, h = 21 yd

So,

Volume of a cylinder = π × r² × h

= 3.14 × 19² × 21

= 3.14 × 361 × 21

= 23,804.34 cubic yard

Ultimately, 23,804.34 cubic yard is the volume of the given cylinder.

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To find:-

Answer:-

We are here given that 1 gallon of paint can be used to paint 400 sq ft. of an area .

There are 4 walls in a room and the area of opposite walls are equal.

So let's find out the area of wall ABCD , its area would be equal to the area of the wall EFGH . So ,

Area of wall ABCD and EFGH :-

Area = lb

Area = 18ft * 8ft

Area = 144ft.²

Therefore area of wall EFGH will also be 144ft.² .

===============================================

Again,

Area of wall DAHE and CBGF :-

Here both the areas of the wall would again be equal, as they have same dimensions of 14ft × 8ft .

Area = lb

Area = 14ft * 8ft

Area = 112ft.²

Therefore area of walls DAHE and CBGF is 112ft.²

==============================================

Calculating total area of the four walls :-

Total area = 2( 112ft.² + 144ft.² )= 512ft.²

Hence total area of four walls is 512ft.²

Now since there will be two coats of paints , total area to be painted would become double that is 1024ft.²

Now we may use Unitary Method :-

To paint 400ft.² 1 gallon of paint is needed.

To paint 1ft.² 1/400 gallon of paint is needed.

To paint 1024ft.² , 1/400*1024 = 2.56 gallons of paint would be needed.

Hence the total paint required is 2.56 gallons.

and we are done!

Answer:

3 one-gallon containers of paint.

Step-by-step explanation:

First, find the total surface area that needs to be painted.

To find the surface area of the walls of a rectangular room, calculate the area of each of the four walls and then add them together.

The area of a rectangle is the product of its width and length.

For the walls of the given room, the "length" is the height of 8 ft, since we want to paint from the floor to the ceiling.

The room has four walls:

Therefore, the total surface area is:

[tex]\begin{aligned}\textsf{Total surface area}&=2(14 \times 8)+2(18 \times 8)\\&=2(112)+2(144)\\&=224+288\\&=512\;\sf ft^2\end{aligned}[/tex]

Since we want to apply two coats of paint, we need to double the surface area:

[tex]\implies 2 \times 512=1024 \; \sf ft^2[/tex]

Now, we can find how many gallons of paint are needed by dividing the total surface area by the coverage per gallon:

[tex]\implies \dfrac{1024}{400}=2.56\; \sf gallons[/tex]

Therefore, we need 2.56 gallons of paint to paint two coats of each wall of the rectangular room.

Since we cannot buy a fraction of a gallon, we need to round up to the nearest gallon. Therefore, we need to buy 3 one-gallon containers of paint.

The approximate circumference of this Spaceship is equal to 157 meters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

By substituting the given points into the volume of a sphere formula, we have the following;

65,417 = 4/3 × 3.14 × r³

r³ = 65,417/4.1867

Radius, r = ∛15,624.96

Radius, r = 25 meters.

Mathematically, the circumference of a sphere can be calculated by using this mathematical expression:

Circumference of a sphere, C = 2πr

Circumference of a sphere, C = 2 × 3.14 × 25

Circumference of a sphere, C = 157 meters.

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In summary, the force required to give the wheel an acceleration of 4.46 rad/s2 when using a 9.00-cm-diameter sprocket is 8,550.54 N, and the force required when using a 5.58-cm-diameter sprocket is 13,764.83 N.

To answer (a) and (b), we need to determine the rotational inertia of the wheel, then calculate the torque and force required to accelerate the wheel with a given angular acceleration.
The rotational inertia of a wheel with all its mass concentrated on the outside radius can be calculated using the formula I = mr^2, where m is the mass of the wheel and r is its radius. In this case, the radius of the wheel is 63.8/2 cm (31.9 cm) and its mass is 1.71 kg, so the rotational inertia is I = [tex]1.71 * (31.9 cm)^2 = 17,214.939 cm^4.[/tex]
To calculate the torque and force required to accelerate the wheel, we use the equation T = I * alpha, where T is the torque, I is the rotational inertia, and alpha is the angular acceleration. Plugging in the values given in the question, we get[tex]T = 17,214.939 cm^4 * 4.46[/tex] rad/[tex]s2 = 76,954.848 Nm.[/tex]
To calculate the force required to accelerate the wheel, we use the equation F = T / r, where F is the force, T is the torque, and r is the radius of the sprocket. For the 9.00-cm-diameter sprocket, the force required is F = 76,954.848 Nm / 9 cm = 8,550.54 N. For the 5.58-cm-diameter sprocket, the force required is F = [tex]76,954.848 Nm / 5.58[/tex] cm = [tex]13,764.83 N.[/tex]

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Answer: 63056$

Step-by-step explanation: i learned that in school 2 hours ago

a. Total purchase price: 15.The total selling price plus the sales tax.

b. Unit pricing: 18. Locating the best value for your money

c. Comparison shopping: 14. A technique that allows shoppers to compare prices

d. Coupons: 16. Discount

e. Rebates: 16. discount

f. Markdown: 17. regular selling price minus the markdown.

g. Markdown rate: 16. Discount

h. Sale price: 18. Locating the best value for your money

Selling price is the amount of money a customer pays for a product or service. It is the amount that a customer pays for the product or service after any discounts, taxes, or fees have been applied.

a. Total purchase price: The total selling price plus the sales tax. This amount is the total cost the customer pays for the good or service, including any taxes and fees.

b. Unit pricing: The cost per unit of a good or service. This allows shoppers to compare the cost of similar items and make an informed decision about which item offers the best value.

c. Comparison shopping: A technique that allows shoppers to compare prices, quality, and other factors when making a purchase.

d. Coupons: A form of discount that can be used when making a purchase. Coupons are often found in newspapers, magazines, or online and can be used to reduce the total purchase price.

e. Rebates: A form of discount where customers receive money back after making a purchase. Rebates are often found in the form of a check or a prepaid debit card.

f. Markdown: The regular selling price minus the markdown. The markdown is the amount that is discounted from the regular selling price.

g. Markdown rate: The percentage of the regular selling price that is discounted. This rate is used to calculate the amount of the markdown.

h. Sale price: The discounted price of a good or service. This is the amount the customer pays after any discounts or coupons have been applied.

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the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.

The formula for radioactive decay is given by:

a = [tex]e^(-kt)\\[/tex] * A

where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.

We can use the given information to solve for k as follows:

When t = 0, a = A. So, we have:

A = [tex]e^(0 * k)[/tex] * A

Simplifying this gives:

1 = e^0

Therefore, we can see that k = 0 at the start of the decay process.

Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:

550 = [tex]e^(-8k)[/tex] * 700

Dividing both sides by 700 and taking the natural logarithm of both sides, we get:

ln(550/700) = -8k

Simplifying this gives:

k = ln(700/550)/8

Using a calculator, we can evaluate this expression to get:

k ≈ 0.0445

Therefore, the decay constant for this material is approximately 0.0445.

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Answer:

x = 3, y = 4

Step-by-step explanation:

Substitute 4x - 8 in for y and then solve for x:

4x + 2(4x - 8) = 20

Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.

Once you have x, you can solve for y.

y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4

So, x = 3, y = 4

Answer:

A = 196 units²

Step-by-step explanation:

the area (A) of a regular polygon is

A = [tex]\frac{1}{2}[/tex] perimeter × apothem

here perimeter = 56 and apothem = 7 , then

A = [tex]\frac{1}{2}[/tex] × 56 × 7 = 28 × 7 = 196 units²

The value of both numbers in fractions will be 207/2 and 207/2.

Given that:

Equation: x + y = 207

The two numbers' product is:

P = xy

P = x(207 - x)

P = 207x - x²

Differentiating P with regard to x. Then we have

dP/dx = 0

207 - 2x = 0

x = 207/2

Then the other number is calculated as,

x + y = 207

207/2 + y = 207

y = 207/2

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Answer:

If the ratio of the number of cats to dogs at the animal shelter is 9 to 5, this means that for every 9 cats at the shelter, there are 5 dogs.

We can express this ratio as:

number of cats : number of dogs = 9 : 5

To find the possible number of cats to dogs, we need to look for pairs of numbers that have a ratio of 9:5. Here are some possible pairs:

   9 cats : 5 dogs

   18 cats : 10 dogs

   27 cats : 15 dogs

   36 cats : 20 dogs

   45 cats : 25 dogs

   54 cats : 30 dogs

   ...

We can see that there are infinitely many possible pairs of numbers that have a ratio of 9:5. To narrow down the possibilities, we need more information such as the total number of animals at the shelter or the number of cats or dogs at the shelter.

Answer:

58.3%

Step-by-step explanation:

Since 175 calories out of 300 come from fat, we can just do 175÷300 and multiply by 100 to get the percentage:

[tex] \frac{175}{300} \times 100 = 58.3\% \: (1dp)[/tex]

[tex]\Large\bold{SOLUTION}[/tex]

To find the percentage of calories from fat for one ice cream bar, we need to divide the number of fat calories by the total number of calories, and then multiply by 100 to get the percentage.

First, we know that each ice cream bar contains 300 calories, and 175 of those calories come from fat. So:

[tex]\sf 175\: fat\: calories \div 300\: total\: calories = 0.5833[/tex]

To convert this decimal to a percentage, we multiply by 100:

[tex]\sf 0.5833 \times 100 = 58.33\%[/tex]

Therefore, the percentage of calories from fat for one ice cream bar is 58.33%.

[tex]\rule{200pt}{5pt}[/tex]

Random sample of size is selected from a population:

The sample statistic that is calculated for the sample values serves as the foundation for the sampling distribution. To estimate the population percentage, the sample proportion, a sample statistic, is computed from the sample values.

In statistics, a simple random sample is a subset of individuals selected at random from a larger population with an equal probability of selection.

Given that we have,

n = 100

p = 0.40

a) The expected value of the sample proportion is defined as:

E(p) = p = 0.40

b) The standard error of the sample proportion is defined as:

[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]

= [tex]\sqrt{\frac{0.40(1-0.40)}{100} }[/tex]

S.E = 0.0024.

c) The sample proportion's sampling distribution follows a normal distribution, with an expected value of 0.40.

E(p) = 0.40

d) According to the central limit theorem, as the sample size approaches infinity, the sample statistic (sample percentage) tends to the population parameter (population proportion).

so,

p ∼ N ([tex]p, \frac{p(-p)}{n}[/tex]) as n → ∞.

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Complete question:

A random sample of size 100 is selected from a population with p = 0.40 .

a. what is the expected value of p (to decimals)? .

b. what is the standard error of p (to decimals)?

c. show the sampling distribution of p

d. what does the sampling distribution of show?

Answer:

16%

Step-by-step explanation:

translation

x% times 2800 = 448

x% = 448 divided by 2800

x% = 0.16 = move decimal 2 spaces to the right = 16%

To find the commission rate we just have to divide the total commission by the total amount of merchandise sold. The commission was $448 and the amount of merchandise sold was $2800.

[tex]\dfrac{448}{2800}=0.16[/tex]

Then, to rewrite a decimal as a percentage, we just need to multiply the number by 100.

[tex]0.16=\dfrac{0.16\times100}{100} =\dfrac{16}{100} =16\%[/tex]

The commission rate is 16%.

Answer:

400

Step-by-step explanation:

480-80=400

Answer

x=6

Step-by-step explanation:

80*x=480

80*6=480

Andy has 15 coins made up of quarters and half dollars, and their total value is $5.00.

He has 10 quarters and 5 half dollars.

To find this answer, we can set up the following equation: 0.25Q + 0.50H = 5.00, where Q represents the number of quarters and H represents the number of half dollars. Solving for Q, we get Q = 10. Therefore, Andy has 10 quarters and 5 half dollars.

To solve this equation, we can use algebra to isolate the variable Q. We can start by subtracting 0.50H from both sides, giving us 0.25Q = 5.00 - 0.50H.

Next, we can divide both sides by 0.25, giving us Q = (5.00 - 0.50H) / 0.25. Therefore, we can substitute the values for 5.00 and 0.50H and solve for Q, giving us Q = 10.

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Answer:

20%

Step-by-step explanation:

80 - 64 = 16

16 ÷ 80 = 0.2

0.2 × 100 = 20%

The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Given that

T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)

Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.

This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.

Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:

(x', y') = (-x, -y)

Using the above, the image is

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

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Complete question

Rotate the figure 180 degrees about the origin

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th

T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)

T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)