Determine which three out of the six points shown below are a solution to the equation 2x + 3y = 16. Plot the three points that are in the solution set, draw a line through the three points and then answer the questions below. (-3,3), (5,2), (1,9), (2,4), (-5,0), (-1,6)

The other Washington DC landmark with coordinates (8,-10) is located in the fourth quadrant of the map.

To determine in which quadrant of the map a point with coordinates (8,-10) is located, we need to look at the signs of the x and y coordinates.

Since the x-coordinate (8) is positive and the y-coordinate (-10) is negative, this point is located in the fourth quadrant.

In general, the four quadrants of a Cartesian coordinate system are divided by the x and y-axes.

The first quadrant is located in the upper right-hand corner and contains points with positive x and y coordinates.

The second quadrant is located in the upper left-hand corner and contains points with negative x and positive y coordinates.

The third quadrant is located in the lower left-hand corner and contains points with negative x and y coordinates.

Finally, the fourth quadrant is located in the lower right-hand corner and contains points with positive x and negative y coordinates.

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The P-value for the hypothesis test is 0.1034 .Round to two decimal places, the P-value is 0.10

To find the P-value for this hypothesis test, we need to use the sample proportion of on the road cars that are 10 years or older, which is the number of cars in the sample that are 10 years or older divided by the total number of cars in the sample. In this case, the sample proportion is \(\frac{357}{1500}= 0.238.\)

We can then use this sample proportion to calculate the P-value, which is the probability of observing a sample proportion as extreme as the one we have seen, or even more extreme, given that the null hypothesis is true. In this case, the null hypothesis states that the true proportion of on the road cars that are 10 years or older is 0.25, so we need to calculate the probability of seeing a sample proportion as low as 0.238, or lower, if the true proportion is actually 0.25.

To do this, we can use a one-sided test, since we are only interested in the probability of seeing a sample proportion lower than 0.25. We can use a normal approximation to the binomial distribution to calculate the P-value.

The standard error of the sample proportion is given by the formula:

SE \(= \sqrt\frac {p \ * (1 - p)}{n}\)

Where p is the null hypothesis value for the proportion (0.25 in this case) and n is the sample size (1500 in this case). Plugging these values into the formula gives us:

SE = \(\sqrt\frac{0.25 * (1 - 0.25)}{1500}= 0.0158\)

The z-score for the sample proportion is then given by the formula:

z =\(\frac{ (p - p_0)}{SE}\)

Where p is the sample proportion (0.238 in this case) and p0 is the null hypothesis value for the proportion (0.25 in this case). Plugging these values into the formula gives us:

\(z = \frac{(0.238 - 0.25)}{0.0158} = -1.27\)

We can then use the z-score to calculate the P-value. Since we are performing a one-sided test, we only need to consider the probability of seeing a sample proportion lower than 0.25. This is given by the area under the normal curve to the left of the z-score. We can use a z-table or a calculator to find this probability.

The probability for a z-score of -1.27 is about 0.1034. This is the P-value for the hypothesis test.

Round to two decimal places, the P-value is 0.10

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15 -differences between gymnosperms and angiosperms:

16-

17- Uniform acceleration is a change of equal velocity in equal interval of tine.

Non- Uniform acceleration is a change of unequal velocity in equal interval of time.

18- Three equation of motion:

Answer:

9^-3/9^12

Step-by-step explanation:

Note that the roots of the equation Unequal and rational (Option D)

The roots of the equation   (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.

x - 3 = ±√4

⇒ x - 3 = ±2

Solve for x

For the positive square root.

x - 3 = 2

x = 2 + 3

x = 5

For the negative square root.

x - 3 = -2

x = -2 + 3

x = 1

Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The roots of the equation (x - 3)² = 4 are

A.Unequal and irrational.

B.Equal and rational.

C.  Equal and irrational.

D.  Unequal and rational.

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

60

Step-by-step explanation:

180 - 120 = 60

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Step-by-step explanation:

y = -1/2 X + 1/4

comparing with y = mx+c

m = -1/2 and m is slop

henve slope = -1/2

we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $\(570.\)

To calculate the total cost of the car rental, we need to first determine the rental rate for a compact car for 8 days, including the optional insurance.

The daily rental rate for a compact car is $ \(56,\) and the optional insurance costs $10 per day. Therefore, the total daily cost of renting a compact car with insurance is:

\(56 + 10 = 66\)

To determine the total cost of renting the compact car for 8 days, we simply multiply the daily cost by the number of days:

\(66 \times 8 = $528\)

Next, we need to determine the cost of gasoline if Nate returns the car without a full tank. The gasoline charge is $ \(3.50\) per gallon, but we don't know how many gallons Nate will need to fill up the tank.

If we assume that a compact car has a gas tank capacity of around 12 gallons, and that Nate will need to refill the tank to its full capacity, then the gasoline charge would be:

$\(3.50 \times 12 = $42\)

Finally, we can calculate the total cost of the rental, including the optional insurance and the gasoline charge if Nate returns the car without a full tank:

$\(528 + $42 = $570\)

Therefore, the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $\(570\).

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Answer:

A = 25 in²

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Define

Side length = 5 in

Step 2: Solve for A

And we have our final answer!

Answer:

25 inches squared.

Step-by-step explanation:

Since we know a square has 4 sides of equal length, and one of the sides has been given to us (5 inches), it's safe to assume the rest of the sides are the same. To find the area, we multiply length x width (5 x 5) to get 25 inches squared. Hope this helps! xx

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

An equation is an expression that shows the relationship between two or more numbers and variables.

The zeros of the function is at:

g(x) = 0, hence:

x³ - x² - 4x + 4 = 0

(x - 1)(x² - 4) = 0

(x - 1)(x + 2)(x - 2) = 0

x = 1, x = -2 and x = 2

The y intercept is at x = 0, hence:

g(0) = 0³ - 0² - 4(0) + 4 = 4

The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.

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we are given a right triangle with one side and one angle known, we are asked to find the other two sides. We can make use of trigonometric functions to find one of the sides. We will use tangent to find side "x", since this function relates the opposite and adjacent sides of the triangle. The function would be like this:

Solving fo "x", we get:

Now, the exact value of "tan 60" is the following:

Replacing that in the equation for "x", we get:

Therefore, x = 10.

To find the value of "y" we can use the Pythagorean theorem, which relates the hypotenuse with the other two sides, like this:

solving the operations we get:

Taking square root on both sides, we get:

Therefore, y = 20

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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Answer:

2362 dollars for all the students

Step-by-step explanation:

my big brain

Answer:

ya you are right okokgudcv

Answer:

Every decimal number can be represented as a rational number.

Answer: Every decimal number can be represented as a rational number.!!!! Hope these helped

Step-by-step explanation:

The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.

Area = length × width

Area = 11.2 cm × 5.1 cm

Calculating the product, we get:

Area = 57.12 cm²

Therefore, the area of the rectangle is 57.12 cm².

The correct answer is: 57.12 cm².

It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.

So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

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His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

Two or more expressions with an Equal sign is called as Equation.

Sheldon wants to buy two shirts at the store.

They were each originally $14.99, but one of the shirts is on sale this week for 10% off.

A 6% sales tax is applied to the total cost of the shirts.

0.90 • 14.99 + 14.99 • 1.06 = n

The first term in the equation, 0.90 • 14.99, represents the cost of the shirt that is on sale.

The 10% discount is applied to the original price of $14.99, which is why we multiply by 0.90.

This term calculates the discounted price of the first shirt.

The second term in the equation, 14.99 • 1.06, represents the cost of the second shirt, plus the 6% sales tax that is applied to both shirts.

This term calculates the total cost of the second shirt with sales tax.

Hence, His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

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The requried population increased by approximately 60.53%.

To find the absolute increase, we subtract the initial population from the final population:

Absolute increase = Final population - Initial population

Absolute increase = 6100 - 3800

Absolute increase = 2300

Therefore, the population increased by 2300 people.

To find the relative increase, we first calculate the percent change:

Percent change = (New value - Old value) / Old value x 100%

Percent change = (6100 - 3800) / 3800 x 100%

Percent change = 2300 / 3800 x 100%

Percent change = 60.53%

Therefore, the population increased by approximately 60.53%.

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a) upward

b) (-3, 1)

c) x intercept: none

y -intercept: (0, 5)

d) x = -3

a) The parabola opens upward

b) Coordinates of the vertex: (h, k)

c) x intercept is the value of x when y = 0

The parabola has no line crossing the x axis. Hence, it has no x intercepts

x intercept: none

y intercept is the value of y when x = 0

The line crosses the y axis at y = 5

when x = 0, y = 5

y - intercept: (0, 5)

d) Axis of symetry is the point a vertical line divides the parabola at the vertex.

The vertical line cuts the parabola into equal halves (mirror images) at x = -3

The equation of axis of symmetry is x = -3

9514 1404 393

Answer:

  cos(-π/8) = (√(2+√2))/2

Step-by-step explanation:

The half-angle formula is ...

  \(\cos{\dfrac{\theta}{2}}=\pm\sqrt{\dfrac{1+\cos{\theta}}{2}}\)

Since cosine is an even function, cos(-π/8) = cos(π/8).

For θ/2 = π/8, θ = π/4 and cos(θ) = (√2)/2. Filling in the formula, we have ...

  \(\cos{(-\dfrac{\pi}{8})}=\cos{\dfrac{\pi}{8}}=\sqrt{\dfrac{1+\cos{\dfrac{\pi}{4}}}{2}}=\sqrt{\dfrac{1+\dfrac{\sqrt{2}}{2}}{2}}\\\\=\sqrt{\dfrac{2+\sqrt{2}}{4}}=\boxed{\dfrac{\sqrt{2+\sqrt{2}}}{2}}\)

Answer:

2646

Step-by-step explanation:

is the correct answer for This question

The required equivalent expression is (216 x 16).

The correct is D.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one maths operation. Addition, subtraction, multiplication, or division are all examples of maths operations. An expression's structure is as follows:

(Number/variable, Math Operator, Number/variable) is an expression.

We have the Expression as,

6³ x 4²

Now, expand the exponents as

6³

= 6 x 6 x 6

= 216

and, 4² = 4 x 4 = 16

Thus, the required equivalent expression is (216 x 16).

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Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then  R(t) = 20 + 1.6sin(2πt/5.2).

The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.

In this case, the amplitude is 1.6.

Since the radius changes by a maximum of 1.6 million miles.

The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)

The phase shift is 0, since when t = 0 the radius is increasing.

The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)

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Answer:

A

Step-by-step explanation:

16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

A division is a process of splitting a specific amount into equal parts.

If it gives a result of -4 then our equation will have ___ = -4

If we subtract 8 from the quotient of a number and 4 we have  x/4 - 8

Our equation is:

x/4 - 8 = -4    

Add 8 to both sides

x/4=-4+8

x/4=4

Multiply both sides by 4

x=16.

Hence, 16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

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Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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Answer:

?

Step-by-step explanation:

To find:-

Answer:-

We are here given that,

\(\implies x^2 + 25 = 0 \)

Subtract 25 from both sides,

\(\implies x^2 = 0 - 25\)

\(\implies x^2 = -25 \)

Take square root on both sides ,

\(\implies x =\sqrt{-25} \)

\(\implies x =\sqrt{ 5^2 (-1) } \)

\(\implies x =\sqrt{5^2} \sqrt{-1} \)

\(\implies x = \pm 5\sqrt{-1}\)

\(\implies x = \pm 5i \)

Seperate the two roots ,

\(\implies \underline{\underline{ x = +5i \ , \ -5i }} \)

Hence the roots of the given equation are 5i and -5i .

and we are done!