In 2006, 95% of new cars in the US came with a spare tire. In 2017, 72% came with a spare tire.
Suppose a researcher takes separate random samples of 250 cars made in each year, then looks at the
difference between the sample proportions P2006 - P2017 of cars with spare tires in each sample.
What are the mean and standard deviation of the sampling distribution of P2006 - P2017?

Choose 1 answer:

A. mean of P2006-P2017: 57.5

Standard Deviation of P2006-2017: Square root of .95(.05)/250 + .72(.28)/250


B C and D in picture

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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Therefore, it has been established that the vectors m = (0, 5) and n = (-2, 1) span the entire vector space R².

To prove that vectors m = (0, 5) and n = (-2, 1) span the vector space R², we need to show that any vector in R² can be expressed as a linear combination of these two vectors.

Let's take an arbitrary vector v = (a, b) in R², where a and b are real numbers.

We can express v as a linear combination of m and n as follows:

v = xm + yn,

where x and y are scalar coefficients.

Substituting the values of m and n, we have:

(a, b) = x(0, 5) + y(-2, 1),

(a, b) = (0, 5x) + (-2y, y),

(a, b) = (-2y, 5x + y).

In order for this equation to hold for any vector (a, b) in R², we must be able to find suitable values for x and y that satisfy the equation.

By comparing the components, we have the following system of equations:

-2y = a,

5x + y = b.

Solving this system of equations, we find:

y = -a/2,

x = (b - y)/5.

Now, substituting these values of x and y back into the equation, we have:

(a, b) = (-2(-a/2), 5((b - (-a/2))/5) + (-a/2)),

(a, b) = (a, b).

Since the original vector v = (a, b) is equal to the linear combination of m and n, we can conclude that any vector in R² can be expressed as a linear combination of m and n.

Therefore, vectors m = (0, 5) and n = (-2, 1) span the vector space R².

Hence, we have proven that the vectors m = (0, 5) and n = (-2, 1) span the vector space R².

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Answer:   \(\bold{a)\ y=\dfrac{9}{7}x+\dfrac{18}{7}}\)

                b) y = 3x - 6

Step-by-step explanation:

Median is the line from the Vertex to the Midpoint of the opposite side

a)

Step 1: Find the Midpoint of QR:

  Q = (4, 6)  R = (5, -3)

   \(x_M=\dfrac{x_Q+x_R}{2}\qquad \qquad \qquad y_M=\dfrac{y_Q+y_R}{2}\\\\\\x_M=\dfrac{4+5}{2}\qquad \qquad \qquad \qquad y_M=\dfrac{6+(-3)}{2}\\\\\\x_M=\dfrac{9}{2} \qquad \qquad \qquad \qquad \qquad y_M=\dfrac{3}{2}\)

              \(Midpoint_{QR}=\bigg(\dfrac{9}{2},\dfrac{3}{2}\bigg)\)

Step 2: Find the slope (m) for P (-2,0) to Midpoint of QR:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{\frac{9}{2}-0}{\frac{3}{2}-(-2)}\\\\\\m=\dfrac{\frac{9}{2}}{\frac{7}{2}}\\\\\\m=\bigg{\dfrac{9}{7}}\)

Step 3: Find the equation of the line from P to Midpoint of QR:

\(y-y_P=m(x-x_P)\\\\\\y-0=\dfrac{9}{7}\bigg(x-(-2)\bigg)\\\\\\\\\large\boxed{y=\dfrac{9}{7}x+\dfrac{18}{7}}\)

**************************************************************************************

b)

Step 1: Find the Midpoint of PR:

  P = (-2, 0)  R = (5, -3)

   \(x_M=\dfrac{x_P+x_R}{2}\qquad \qquad \qquad y_M=\dfrac{y_P+y_R}{2}\\\\\\x_M=\dfrac{-2+5}{2}\qquad \qquad \qquad \qquad y_M=\dfrac{0+(-3)}{2}\\\\\\x_M=\dfrac{3}{2} \qquad \qquad \qquad \qquad \qquad y_M=-\dfrac{3}{2}\)

              \(Midpoint_{PR}=\bigg(\dfrac{9}{2},\dfrac{3}{2}\bigg)\)

Step 2: Find the slope (m) for Q (4,6) to Midpoint of PR:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{6-(-\frac{3}{2})}{4-(\frac{3}{2})}\\\\\\m=\dfrac{\frac{15}{2}}{\frac{5}{2}}\\\\\\m=\bigg{3}\)

Step 3: Find the equation of the line from Q to Midpoint of PR:

\(y-y_Q=m(x-x_Q)\\\\\\y-6=3(x-4)\\\\\\y-6=3x-12\\\\\\y=3x-12+6\\\\\\\large\boxed{y=3x-6}\)

Answer:

4*6 is 24

its like 6 circles with 4 dots inside and you just count all the dots or it could be the other way around.

If total cost for tuition plus room and board at state university is 2,584 dollars and  tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars

Given,

The total cost for tuition plus room and board = 2584 dollars

Consider the cost for room and board as x

Tuition costs 704 dollars more than room and board.

Therefore the tuition fees = 704+x

Then the total cost = Cost for tuition fees+ Cost for room and board

2584 = (704+x)+x

2584= 704+2x

2x= 1880

x= 940  dollars

Then the tuition fees = 704+x

=704+940

=1644 dollars

Hence, if total cost for tuition plus room and board at state university is 2,584 dollars and  tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars

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Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step:

\((12 - 9)^{2} + \frac{15}{3} \\ (3) ^{2} + \frac{15}{3} \\ 9 + \frac{15}{3} \\ 9 + 5 \\ = 14\)

Point A on the number line represents the number fraction -1. Option A is correct.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
A number line goes from negative 1 to positive 1. There are 3 equal spaces between each number. Point A is 1 mark to the left of 0.
So on the number line, the numbers on the left of 0 follow the negative sequence, and the number to the right of the zero follows the positive sequence. Following the given condition, point A on the number line represents the number fraction -1.

Thus, Point A on the number line represents the number fraction -1.

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The difference between the linear and projectile motion is that "Linear-motion" refers to motion of object in a "straight-line", while "projectile-motion" refers to motion of an object that is thrown into air, in a curved path.

In linear motion, the object moves along a straight line, with its velocity and acceleration aligned in the same direction. The object's speed and direction may change, but its motion remains linear.

In projectile motion, the object moves along a curved path under the influence of gravity. The object is launched into the air with an initial velocity, and then gravity causes it to follow a parabolic path until it lands back on the ground. The motion of the object is influenced by both its initial velocity and the force of gravity.

In both linear and projectile motion, the "horizontal-component" of velocity will usually remain constant because there is no external force acting on the object in horizontal direction, and thus no acceleration.

Therefore, the object will continue to move at a constant velocity in the horizontal direction, as long as there is no external force acting on it.

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The area of the triangular yard is 7000 ft².

The entire area enclosed by three sides of a triangle is the area of it.

Given,

The base of the triangle is 200 feet and the height of the triangle is 70 feet.

Therefore, the area of the triangle

= (1/2) × base of the triangle × height of the triangle =  (1/2) × 200 × 70 ft² = 7000 ft².

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a = 2(√2 + √10)/√3 and b = 4(√2 - √10) are the required values of sides a and b respectively.

Given,
A = π/6
B = 8π/9
C = π - A - B = π - π/6 - 8π/9 = 5π/18
c = 4
In order to find sides a and b, we will use sine rule which states that for a triangle with sides a, b and c and angles A, B and C respectively,
a/sinA = b/sinB = c/sinC
Applying the above formula, we get:
a/sinA = c/sinC
a/sin(π/6) = 4/sin(5π/18)
a/(1/2) = 4/(√2 + √10)/4
a = 2(√2 + √10)/√3
b/sinB = c/sinC
b/sin(8π/9) = 4/sin(5π/18)
b/(√2 - √10)/2 = 4/(√2 + √10)/4
b = 4(√2 - √10)

Therefore, a = 2(√2 + √10)/√3 and b = 4(√2 - √10) are the required values of sides a and b respectively.Summary:Given, A = π/6, B = 8π/9, C = π - A - B = π - π/6 - 8π/9 = 5π/18 and c = 4. To find sides a and b, we used the sine rule. Finally, a = 2(√2 + √10)/√3 and b = 4(√2 - √10) are the required values of sides a and b respectively.

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According to the question we have our assumption must be false and there are indeed infinitely many primes of the form 4k+3.

To prove that there are infinitely many primes of the form 4k+3, where k is a nonnegative integer, we can use a proof by contradiction. Assume that there are only finitely many primes of this form, say p1, p2, p3, ..., pn.

Consider the number N = 4(p1p2p3...pn) - 1. This number is of the form 4k+3, since the product of primes is also of this form.

Now, any prime factor of N must also be of the form 4k+3, since any prime factor of N cannot be 2 (since N is odd) and it cannot be of the form 4k+1 (since N leaves a remainder of 3 when divided by 4).

However, this contradicts our assumption that p1, p2, p3, ..., pn are the only primes of the form 4k+3, since N is a prime greater than pn and is also of this form.

Therefore, our assumption must be false and there are indeed infinitely many primes of the form 4k+3.

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Answer:it’s -2

Step-by-step explanation:

Did on apex lol

Step-by-step explanation:

1/8+1/2make both denominators 8

in 1/2 multiply both the numerator and the denominator by 4to get 4/8

1/8 + 4/8=5/8

Answer:

two

Step-by-step explanation:

The partial fraction decomposition of x² + 5 (x − 3)(x² + 4) can be written in the form of f(x) = C/(x - 3) and g(x) = (Ax + B)/(x² + 4), where f(x) is a constant function and g(x) is a linear function.

partial fraction decomposition, we break down the given expression into simpler fractions. The expression x² + 5 (x − 3)(x² + 4) has a quadratic term x² and a linear term x, suggesting that the decomposition will involve a constant function and a linear function.

Step 1: Factorize the expression x² + 5 (x − 3)(x² + 4):

x² + 5 (x − 3)(x² + 4) = x² + 5 (x³ - 3x² + 4x - 12)

Step 2: Expand the expression:

= x² + 5x³ - 15x² + 20x - 60

Step 3: Set up the partial fraction decomposition:

x² + 5x³ - 15x² + 20x - 60 = C/(x - 3) + (Ax + B)/(x² + 4)

Step 4: Combine the fractions on the right-hand side:

x² + 5x³ - 15x² + 20x - 60 = [C(x² + 4)] + [(Ax + B)(x - 3)] / (x - 3)(x² + 4)

Step 5: Equate the coefficients of corresponding terms:

x² + 5x³ - 15x² + 20x - 60 = C(x² + 4) + (Ax² - 3Ax + Bx - 3B) / (x - 3)(x² + 4)

Step 6: Compare coefficients:

For the constant term: 0 = 4C - 3B

For the linear term: 0 = A + B - 15A

For the quadratic term: 1 = C + A

Solving the system of equations, we find that f(x) is a constant function given by f(x) = C/(x - 3), where C = 1, and g(x) is a linear function given by g(x) = (Ax + B)/(x² + 4), where A = -1 and B = -4.

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The value of "n" is 6.

"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:

7(n+4) = 5(n+8)

Expanding the brackets, we get:

7n + 28 = 5n + 40

Simplifying, we get:

2n = 12

n=6

A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.

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Since the relationship is proportional, the line will pass through the origin (0, 0). This means that if there is a bag with zero weight, it would have zero cost.

To graph the proportional relationship between the weight and total cost of the bags of lemons, follow these steps:

1. Identify the independent variable and the dependent variable. In this case, the weight of the bag (in pounds) is the independent variable, and the total cost of the bag (in dollars) is the dependent variable.

2. Create a coordinate plane. Label the x-axis as "Weight (pounds)" and the y-axis as "Total Cost (dollars)".

3. Plot the data points. For the first bag, with a weight of 2.4 pounds and a cost of $5.28, plot a point at (2.4, 5.28) on the coordinate plane. For the second bag, with a weight of 2.7 pounds and a cost of $5.94, plot a point at (2.7, 5.94) on the coordinate plane.

4. Draw a straight line passing through the two plotted points. This line represents the proportional relationship between the weight and total cost of the bags of lemons.

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Answer:

$ 612 is her monthly payment

Step-by-step explanation:

$3,600/6 = 600

600 + 12 = 612

Answer:600

Step-by-step explanation:

The total number of possible outcomes containing exactly 3 heads when a coin is flipped eight times where each flip comes up either heads or tails are 56.

There are two possible outcomes i.e. heads and tails when a coin is flipped. If the coin is flipped 8 times, the total number of outcomes will be:-

\(2^8=256\)

We need exactly 3 heads , and hence exactly 5 tails, like

H H H T T T T T

Here H represents heads and T represents tails.

But H and T can come in any combination, for example:-

H T H H T T T T

Hence, total possible outcomes containing exactly 3 heads and 5 tails will be determined using the combinations formula :-

\(^{8}C_{3}=\frac{8!}{3!5!}=\frac{8*7*6*5!}{3*2*5!}=8*7=56\)

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Answer:

A. Line r intersects line p

Step-by-step explanation:

to find the second graph multiply the slope of line p by -10

slope is 1/5 or 0.2

So,

0.2 * -10 = -2

slope of second line is -2

Graph shown

Altered line shown in blue

Line p shown in green

As you can see, they intersect and meet no other answers

The bicycles produced from the beginning of week 2 to the end of week 3 are 2926.

To find the number of bicycles produced from the beginning of week 2 to the end of week 3, we will use the given production function P(t) = 95 + 588t^2 - 14t, where t is the number of weeks.

First, we need to find the number of bicycles produced by the end of week 2 and week 3.

To do this, we'll plug in t = 2 and t = 3 into the production function:

P(2) = 95 + \(588(2)^{2}\) - 14(2) = 95 + 588(4) - 28 = 95 + 2352 - 28 = 2419 bicycles

P(3) = 95 + \(588(3)^{2}\) - 14(3) = 95 + 588(9) - 42 = 95 + 5292 - 42 = 5345 bicycles

Now we need to find the difference between the bicycles produced by the end of week 3 and those produced by the end of week 2:

Number of bicycles produced from the beginning of week 2 to the end of week 3 = P(3) - P(2) = 5345 - 2419 = 2926 bicycles

So, the factory produced 2926 bicycles from the beginning of week 2 to the end of week 3.

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Answer:

The answer is kilogram

Step-by-step explanation:

The answer is a kilogram because a kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams). A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters). A dekaliter is 10 times larger than one liter (so 1 dekaliter = 10 liters).

Hope this helps!!

The Standard Form of the polynomial function 3x^2 4x + 7x^3 + 1 is 7x^3 +3^2 +4x + 1

The meaning of the Standard Form of polynomial function can be explained as when the terms are in this equation or functions are be written in descending order of exponents.

This is usually done starting from the from left to right, we were given the function as :3x^2 +4x + 7x^3 + 1  , then let us arrange it as:

7x^3 +3^2 +4x + 1

Therefore, the Standard Form of polynomial function is 7x^3 +3^2 +4x + 1 .

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Answer:

36 people joined the radio control club.

Step-by-step explanation:

15-3= 12

12*3=36

Answer:

Step-by-step explanation:

7R - 6 + 4R + 7 = 5X + R

A. 2,5

B. 141

C. 12, + 5+1

D. 124 + 47+1​

THE ANSWER IS

11R + 1 = 5X + R

-12X -- 66y + 10
_____________
           45

Answer:

y > 1/3x -3

Step-by-step explanation:

Just find the equation of the line, which is y = 1/3x -3, and then determine what the symbol is going to be. Since the line is dotted, it will either be < or >. When the shaded area is on top of the line, it's >. Remember that by saying left on the bottom or right on top.