Every attendant at a town's Chili Cook-off received a raffle ticket. There were 9 raffle prizes,
including 7 that were gift certificates to restaurants.
If 6 prizes were randomly raffled away in the first hour of the cook-off, what is the probability
that all of them are gift certificates to restaurants?

The standard form of the hyperbola is:

(x-3)²/4 - (y+2)²/(64/35) = 1

Given vertices (1, -2) and (5, -2), the center is (3, -2) and the semi-major axis, a = 2.

The hyperbola is horizontal.

Using point (-3, 6), we find the semi-minor axis, b² = 64/35.

The standard form of the hyperbola is:

(x-3)²/4 - (y+2)²/(64/35) = 1

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Answer:

A.the annual premium can be found by multiplying the monthly premium by 12:

Annual premium = Monthly premium x 12

Annual premium = $65 x 12 = $780

b. The semiannual premium can be found by dividing the annual premium by 2:

Semiannual premium = Annual premium / 2

Semiannual premium = $780 / 2 = $390

c. To calculate how much less Ronald's semiannual payments would be if he dropped the optional collision insurance, we need to subtract the cost of the optional insurance from the semiannual premium:

Semiannual payment with optional insurance = Semiannual premium - $120

Semiannual payment with optional insurance = $390 - $120 = $270

Semiannual payment without optional insurance = Semiannual premium - $120

Semiannual payment without optional insurance = $390 - $120 = $270

Therefore, Ronald's semiannual payments would be $270 if he dropped the optional collision insurance.

Therefore, the closest option to the calculated percentage is option (d) 44%.

Percent, denoted by the symbol "%", is a way of representing a fraction or proportion out of 100. It is used to express a part of a whole in terms of hundredths. For example, 50% is the same as 50 out of 100, which simplifies to 1/2 or 0.5 as a decimal. Percentages are commonly used in many areas such as finance, statistics, and everyday life to express changes, rates, or comparisons.

Here,

To calculate the percentage of customers who prefer cookies, we need to add up the number of customers who prefer cookies from each survey and divide it by the total number of customers who took the survey.

Number of customers who prefer cookies: 25 + 9 + 28 + 11 = 73

Total number of customers who took the survey: 17 + 11 + 20 + 13 + 25 + 8 + 9 + 30 + 26 + 11 = 170

Percentage of customers who prefer cookies: (73/170) x 100% ≈ 44%

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If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × [tex](0.9225)^{t}[/tex].

An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.

In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).

We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.

The formula for an exponential function is y = a × [tex]b^{t}[/tex], where "a" = initial value and "b" = growth or decay factor.

In this case, the initial area of the forest is = 1500 km², and

The forest is decreasing by 7.75% each year.

So, the "decay-factor" is = 1 - 0.0775 = 0.9225,

The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:

⇒ y = 1500 × [tex](0.9225)^{t}[/tex],

Therefore, the required "exponential-function" is y = 1500 × [tex](0.9225)^{t}[/tex].

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The given graph represents the function with the equation f(x) = 12(x - 1)/[(x + 2)(x - 3)].

To write an equation for the function, we first observe that the vertical asymptotes occur at x = -2 and x = 3, indicating that the denominator (Q(X)) has roots at x = -2 and x = 3. Hence, the equation of the denominator is:

Q(X) = (x + 2)(x - 3)

Furthermore, from the graph, we can see that the zero of the function occurs at x = 3, indicating that the numerator (P(X)) has the factor (x - 3). Let a be the leading coefficient of P(X), so we can write:

P(X) = a(x - 1)(x - 3)

To find the value of a, we use the fact that the y-intercept of the function is (0, -2). Substituting x = 0 and f(0) = -2 into the equation of the function, we get:

-2 = a(-1)/[(2)(-3)]

Simplifying this equation gives us:

a = -2/(2*3) = -1/3

Substituting this value of a into the equation for P(X), we get:

P(X) = (-1/3)(x - 1)(x - 3)

Substituting the equations for P(X) and Q(X) into the formula for f(x), we get:

f(x) = (-4)(x - 1)/[(x + 2)(x - 3)]

Simplifying this equation gives us:

f(x) = -4(x - 1)/[(x + 2)(x - 3)]

Therefore, the equation of the function graphed in the figure is f(x) = -4(x - 1)/[(x + 2)(x - 3)].

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Answer:

Step-by-step explanation:

If cos a = 0.5, then sin a could equal √(1 - cos^2 a) = √(1 - 0.5^2) = √0.75 ≈ 0.866.

Between 2226 and 3241 people are predicted to see an improvement in their baldness.

The expected amount of people expected to see improvement is obtained applying the proportions in the context of the problem.

The sample proportion is given as follows:

175/500 = 0.35.

Considering the margin of error, the bounds are given as follows:

Hence the amounts out of 7810 people are obtained as follows:

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Answer:
here is the graph for it

Step-by-step explanation:

The prominent similar feature between f(x) and g(x) is the present y-intercept.

Since the discriminant is negative, there are no possible solutions to the given equation, which implies that f(x) has no x-intercepts.

It should be noted that to identify the y-intercept, we set x = 0 and evaluate f(x):

f(0) = 2(0)² - 3(0) + 4

f(0) = 4,

The y-intercept of f(x) can be determined as (0, 4).

Moreover, the function g(x) = 2x-4 is a power function having a negative exponent, which makes it a reciprocal function. It's domain comprises all real numbers but 0, while its range includes all real numbers excluding 0.

In order to obtain the x-intercept of g(x), we set g(x) equal to zero and solve for x:

0 = 2x-4

2x = 4

x = 2

Consequently, the x-intercept of g(x) is (2, 0), together with the y-intercept (0, -4).

The prominent similar feature between f(x) and g(x) is the present y-intercept. On the other hand, f(x) does not contain any x-intercepts, whereas g(x) has a single x-intercept. Also, f(x) is categorized as a second-degree polynomial function, whereas g(x) is classified as a reciprocal function.

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The error made by Tony is in Step 4, where he wrote "x + 2 = ± 81". The correct step should be:

Step 4: Take the square root of both sides to solve for x.

√((x + 2)^2) = √81

In this step, Tony should have taken the square root of both sides, but he made the mistake of only taking the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

The correct step should be:

x + 2 = ±9

Step 5: Solve for x.

x + 2 = 9 or x + 2 = -9

Step 6: Subtract 2 from both sides to isolate x.

x = 9 - 2 or x = -9 - 2

This will give the correct solutions:

x = 7 or x = -11

So, the error made by Tony occurred in Step 4 where he only took the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.

Hope this helps!

Answer:

Step-by-step explanation:

y = 5x^3 - x

Slope of a secant

= (y2 - y1)/(x2-x1)     where (x1, y1) and (x2, y2) are the 2 points.

Slope for the interval (1, 2)

= [5(2)^3 - 2)- (5(1)^3 - 1)] / (2-1)

= 34

Slope for interval (1, 1.5)

=  [5(1.5)^3 - 1.5)- (5(1)^3 - 1)] / (1.5-1)

= 22.75

In the same way we get the slopes of the  intervals:

(1, 1.1):-  15.55

(1, 1,01):-  15.15

(1, 1.001):- 15.015

So the answer is 15.

Based on the Tangent Chord Theorem:

The Tangent Chord Theorem states that if a chord and a tangent intersect at the point of tangency, then the measure of each angle formed is equal to half the measure of its intercepted arc.

Considering the given angles;

m∠1 = ¹/₂ AB

m∠1 = ¹/₂ ACB

m∠DEG = ¹/₂ * 308°

m∠DEG = 154°

m∠DBC =  ¹/₂ * (360 - 192)

m∠DBC = 84°

m XY = 360 - (151 * 2)

m XY = 56°

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11. Angle KEF = 40°, Angle KEJ = 50°

12. Angle HEF = 115°, Angle KED = 140°

13. Angle JEF = 90°, Angle KEF = 90°

14.   Angle DEF = 180°

The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.

11.  Acute angles: Those angles are less than 90 degree angles.

     Angle KEF = 40°

     Angle KEJ = 50°

     Angle KEH = 75°

     Angle JEH = 25°

     Angle HED = 65°

12. Obtuse angles: Those angles are more than 90 degree angles.

     Angle HEF = 115°

     Angle KED = 140°

13. Right angle: Those angles are 90 degree angle.

     Angle JEF = 90°

     Angle KEF = 90°

14. Straight angle: Those angles make 180 degree angle.

     Angle DEF = 180°

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There is a probability of 0.117 for at least 2 of the tiles to be vowel tiles.

Given that,

Probability that the tiles getting is a vowel tile is 30%.

P(V) = 30% = 0.3

That is there will be only 3 tiles out of 10 tiles which are vowels.

Out of 8, there will be 8 × 0.3 = 2.4 tiles which are vowels.

There would be either 2 or 3 vowels.

Probability that at least 2 of them is vowel tiles is,

Probability = (0.3)² + (0.3)³

                 = 0.117

Here,

The simulation which can be used to fairly represent the situation is,

Use a computer to randomly generate 8 numbers from 1 to 10. Each time 1, 2 or 3 appears, it represents a vowel tile.

Hence, the required probability is 0.117.

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The transformations that are applied to the graph of the function [tex]f(x) = 10^x[/tex] to produce the graph of the function [tex]g(x) = 3(10)^x - 2[/tex] is: C. a vertical dilation by a factor of 3 and a vertical shift down 2 units.

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a function or object is transformed, all of its points would also be transformed.

In Mathematics and Geometry, a dilation refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Based on the parent function (exponential), we can logically deduce that the exponential function g(x) can be produced by vertically stretching the parent function by a scale factor of 3, followed by a vertical shift down 2 units;

[tex]f(x) = 10^x[/tex]

[tex]g(x) = 3(10)^x - 2[/tex]

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Answer: 86 memory sticks should be purchased

Step-by-step explanation: If he needs to be a stick for each teacher, and there are 86 teachers, then he needs to be 86 sticks.

The probability that Mason does not arrive at work by 9 a.m. is given as follows:

p = 17/50.

A probability is calculated dividing the desired number of outcomes by the total number of outcomes.

The outcomes relating to the bus not arriving on time are divided as follows:

Hence the probability is given as follows:

p = 1/4 x 4/5 + 7/10 x 1/5

p = 1/5 + 7/50

p = 10/50 + 7/50

p = 17/50.

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Answer:

C

Step-by-step explanation:

The theoretical probability of landing on A, B, C, or D is all 1/4. This would also mean the theoretical probability is 45/180. Statement C is the only one that is true.

Answer:

below

Step-by-step explanation:

To show that (AB)^-1 = B^-1A^-1, we need to show that:

(AB)(B^-1A^-1) = (B^-1A^-1)(AB) = I

where I is the identity matrix.

Using the associative property of matrix multiplication, we can simplify the left-hand side of the equation as:

(AB)(B^-1A^-1) = A(BB^-1)A^-1 = AIA^-1 = AA^-1 = I

Similarly, using the associative property of matrix multiplication, we can simplify the right-hand side of the equation as:

(B^-1A^-1)(AB) = B^-1(A^-1A)B = B^-1IAB = BB^-1 = I

Therefore, we have shown that (AB)^-1 = B^-1A^-1.

To show this identity, we need to demonstrate that:

(AB)^-1 = B^-1 A^-1

To do this, we start by multiplying both sides of the equation by (AB):

(AB)^-1 (AB) = B^-1 A^-1 (AB)

On the left side, we know that (AB)^-1 is the inverse of AB. So we can simplify to:

I = B^-1 A^-1 (AB)

Where I is the identity matrix. We can now simplify the right side by rearranging the terms:

B^-1 A^-1 (AB) = B^-1 (A^-1 A) B

Since A^-1 A = I, we can simplify further to:

B^-1 (A^-1 A) B = B^-1 IB = B^-1 B = I

Therefore, we have shown that:

(AB)^-1 = B^-1 A^-1

Q.E.D.

The bar chart showing the growth of the price per tone of ground nut over the years is attached accordingly.

A bar chart, sometimes known as a bar graph, is a type of chart or graph that displays categorical data using rectangular bars with heights or lengths proportionate to the values they represent. The bars can be plotted horizontally or vertically. A vertical bar chart is also known as a column chart.

From the bar chart, is clarer to see that the price of ground nut per tone increased steadily year on year.

By the year 2008, it had hit  record high of 100,000 per ton.

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The cost assigned to the ending inventory will cost or assigned based on the lifo method is attached.

Denoting the valuation of inventories a business owns at the completion of any accounting term – be it monthly, quarterly, or annually – ending inventory speaks to the cost of items that have yet to be sold or used in the creation of goods and services.

Checking a company's economic performance is contingent on examining its ending inventory since this element impacts cost of goods sold (COGS) substantially; many corporations' COGS are worked out by subtracting the cost of goods distributed over a period from the overall cost of goods available for sale during that same interval.

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BGC or AGF

Adjacent means next to or adjoining something else and both of the mentioned angles are next to angle AGB.

The graph that represents the exponential function f(x) = 2^(x - 1) + 2 is given as follows:

Graph A.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function for this problem is defined as follows:

f(x) = 2^(x - 1) + 2

It has an horizontal asymptote at y = 2, which removes the option C.

The parameter b is of b = 2, meaning that the function is increasing, which removes option D.

The numeric value of the function when x = 0 is given as follows:

f(0) = 2^(0 - 1) + 2

f(0) = 1/2 + 2

f(0) = 5/2

f(0) = 2.5.

Hence graph A is correct.

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Answer:

-----------------------

Tangent line is perpendicular to radius at the point of tangency.

Hence we have:

Therefore ΔMKJ is a right  triangle.

Radius is 11, so diameter is 22, this is one of legs and its hypotenuse is 25 units.

Use Pythagorean theorem to find the missing leg:

Answer:

y = 2(x + 1.5)² + 0.5

Step-by-step explanation:

"To convert the standard form y = ax² + bx + c to vertex form:

Extract a from the first two terms: y = a[x² + (b/a)x] + c.

Add and subtract (b/(2a))² inside the bracket: y = a[x² + (b/a)x + (b/(2a))² - (b/(2a))²] + c.

Use the short multiplication formula: y = a[(x + b/(2a))² - (b/(2a))²] + c.

Expand the bracket: y = a(x + b/(2a))² - b²/(4a) + c.

This is your vertex form with h = -b/(2a) and k = c - b²/(4a)."

^^ not my explanation!!

Answer:

3cm

Step-by-step explanation:

triangle formula is height times base divided by two and divide base by two. then its 6 and divide 6 from 18. so the answer is 3cm

Triangles to total shapes because triangles= 5 total, and total shapes = 10. 5/10 simplifies to 1/2

Answer:

True, False, True, False, False (answered top to bottom)

Step-by-step explanation: