1. In basketball, you score 2 points for a basket and 1 point for a free throw. (Assume you never make 3 point
shots) In order to win the game, you need to score at least 15 points. Let x represent the number of baskets that
you make and y represent the number of free throws that you make. How many of each type of shot could you
make to win the game?
a. Write an equation to model the relationship.

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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The given coordinates are actually a rectangle

The coordinates are given as:

A (3, 1), B (1, 5), C (9, 9), and D (11, 5).

Calculate the distance between the coordinates using:

\(d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2\)

So, we have:

\(AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20\)

\(BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80\)

\(CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20\)

\(DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80\)

The above shows that the opposite sides are congruent

Next, we calculate the slopes using:

m = (y2- y1)/(x2- x1)

So, we have:

AB = (1- 5)/(3-1) = -2

BC = (5- 9)/(1-9) = 1/2

CD = (9- 5)/(9-11) = -2

DA = (5- 1)/(11-3) = 1/2

The slopes of adjacent sides are opposite reciprocals.

This means that the sides are perpendicular

Hence, the given coordinates are actually a rectangle

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Answer:

21km

Step-by-step explanation:

1km=100000cm

14x150000=2100000cm=21km

The distance in real life in kilometers by the given scale factor will be 21 kilometers.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

As per the given,

Scale factor = 1 : 150000

It means 1 cm will convert to 150000 cm.

In real life = 14 x 150000 = 2100000 cm

2100000 cm = 21000 m = 21 kilometer

Hence "The distance in real life in kilometers by the given scale factor will be 21 kilometers".

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Answer:

Mov

Step-by-step explanation:

move point b one and one half units to the left

If the least value of n is 4, then the inequality best shows all the possible values of n is, n ≥ 4. So Option B is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The least value of n is 4,

Inequality representation = ?

It is known that,

Least value  of n is 4

So, Minimum possible value of n is 4

Maximum value of n should be more than 4,

In order to satisfy the condition,

So,

n  > 4

By combining both the things,

It can be written as,

n ≥ 4

Hence, the best inequality representation is n ≥ 4

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Answer:

O a=0

Step-by-step explanation:

Answer:

9%

Step-by-step explanation:

To find the increased amount, subtract this month sales from the last month sales.      

Increased amount = 196200 - 180000

                              = £ 16,200

Now, find the increased percentage using the formula,        

\(\boxed{\bf Increased \ percentage = \dfrac{Increased \ amount}{Original \ amount}*100}\\\\\)

                                        \(= \dfrac{16200}{180000}*100\\\\= 9\%\)

Using job costing, the 2018 actual indirect-cost rate is $6.55 per machine hour.

The actual indirect-cost (overhead) rate is the ratio or quotient between the actual overhead costs (dividend) and actual allocation base units (divisor).

This rate is different from the predetermined overhead rate, which is based on the budgeted overhead costs and the budgeted allocation base units.

Direct cost rate per unit = $8.00

Selling price per unit = $25.00

Estimated manufacturing overhead costs = $320,000

Estimated machine hours = 50,000 MHs

Overhead cost-allocation base = Machine hours

Predetermined overhead rate = $6.40 ($320,000/50,000)

Actual manufacturing overhead costs = $360,000

Actual machine hours = 55,000 MHs

The actual indirect-cost rate is $6.55 ($360,000/55,000)

Thus, for 2018, ABC Co's actual indirect-cost rate is $6.55 per machine hour, which is higher than the predetermined overhead rate of $6.40.

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Answer:

C

Step-by-step explanation:

 2

+2

-----

 4

Given parameters:

  Equation:

          (x-4)²=9

Problem, solve the equation by factoring and extracting the root

Solution:

    Given equation:

                  (x-4)²=9

         subtract 9 from both sides to equate to zero;

                (x-4)² - 9 = 0

                (x -4)² - 3² = 0

  Now, this is similar to the concept of difference of two squares;

          x² - y² = (x + y)(x-y)

Here x  = x-4 and y = -3

  So input and solve;

              (x - 4 -3)(x - 4 -(-3)) = 0

              (x - 7)(x - 4+3) = 0

              (x -7)(x -1) = 0

S0,

             x - 7 = 0 or x-1 = 0

             x = 7 or 1

If we extract the square roots;

          (x-4)² = 9

         √(x-4)² = √9

              x - 4 = 3

              x  = 4 + 3 = 7; this is not the only solution to the problem

So we cannot solve it by extracting the square root.

The solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root. The equation can only be solved by factoring

Given the expression;

(x-4)²=9

This expression can be solved by factoring

Factoring the expression on the left hand side

(x-4)(x-4)=9

x²-4x-4x+16 = 9

x² - 8x + 16 - 9 = 0

x² - 8x + 7 = 0

x² -x - 7x + 7 = 0

x(x-1) -7(x-1) = 0

x-7 = 0 and x - 1 = 0

x = 7 and 1

This shows that the expression can be solved by factoring

The other way is by squaring both sides

(√x-4)² = ±√9

x - 4 =±√9

x = -9+4 and x = 9 + 4

x = -5 and 13

Since the solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root

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Answer:

12.259-12.25 890654321

I recommend use of simple random sampling to determine the three possible toppings to be used for the vegetarian pizza.

It is a sampling technique in which each member of the population has an equal chance of being selected for the sample. Here, the population would be students who regularly eat at the school cafeteria.

By using the sampling, we make sure that each student has an equal chance of being selected to taste test the different pizza toppings. This will help to eliminate bias and provide a representative sample of the population's preferences. They will provide feedback which will be used to determine which topping should be used for the vegetarian pizza.

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Answer:

I think its 10:5=2

Step-by-step explanation:

Answer:

I think it would be 214

Step-by-step explanation:

34+34=68

68+34=102

102+34=154

154+60=214

Answer:

yeah u right 214

Step-by-step explanation:

just do the correct steps

This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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First, we can find the 20% of 46.50 by multiplying the cost of the meal by the tip in decimal form:

we have that the tip was $9.3. Adding the cost of the meal and the tip we get:

therefore, the total cost including the tip is $55.8

Answer:

$181.4

Step-by-step explanation:

Note,

Therefore, the store applied a discount price of $181.4 to the set of golf clubs.

Answer:

Multiply/divide both sides by the same non-zero constant

Step-by-step explanation:

5x = 20

Divide each side by 5

5x/5 = 20/5

x = 4

Step-by-step explanation:

This is the second fundamental theorem of calculus.

d/dx ∫ₐᵇ f(x) dx = f(b) (db/dx) − f(a) (da/dx)

This is derived using chain rule:

d/dx g(f(x)) = g'(f(x)) f'(x)

Therefore:

d/dx ∫₀²ˣ arctan(t) dt = arctan(2x) (2x)' = 2 arctan(2x)

Answer: to go about this problem the easiest way for me would be to see what I can multiply to get 81. Imminently I see that 9*9 is 81 and it also adds up to 18 :)

so the answer is 9 and 9  give me a thumbs up if this helped!

Answer:

so z is 9 I guess

Step-by-step explanation:

81/9=9

so z is 9

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

Step-by-step explanation:

You have omitted relevant parts of the question. What is the question? Are you looking for the area of the yard? The amount of fencing needed?

What units are used? (Feet, yards, meters, etc.)

area of yard = 75×55 = 4125 units²

amount of fencing needed = perimeter of rectangle = 2(75+55) = 260 units.

The total length of the fencing is the perimeter of the rectangular yard which is P = 260 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The width of the rectangular yard W = 55 feet

The length of the rectangular yard L = 75 feet

Let the perimeter of the rectangular yard be = P

And , the required fencing = Perimeter of rectangular yard

Perimeter of rectangular yard P = 2 ( L + W )

Substituting the values in the equation , we get;

Perimeter of rectangular yard P = 2 ( 55 + 75 )

Perimeter of rectangular yard P = 2 ( 130 )

Perimeter of rectangular yard P = 260 feet

Therefore , the value of P is 260 feet

Hence , the perimeter of yard is 260 feet

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Mr. Fuller wants to put fencing around his rectangular-shaped yard. the width of the yard is 55 feet and the length is 75 feet. how many feet of fencing does Mr. Fuller

Answer:

  h > 5

  h < 0

Step-by-step explanation:

We suppose that a "Special Solution" inequality is one that is technically incorrect, but is written using a compact "shorthand" form.

As written, the inequality claims that 17 < 2, which is false. There can be no value of the variable that will make this true. We presume the intended meaning is ...

  17 < 3h +2   or   3h +2 < 2

Subtracting 2 from the inequality gives ...

  15 < 3h < 0

Dividing by 3 gives ...

  5 < h < 0

There is no value of h that is both greater than 5 and less than 0, so we presume this means the OR (union) of the solution sets ...

  h > 5

  h < 0

Answer: 3

Step-by-step explanation:

2/3 4/6

25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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Answer:

H0:p1=p2; Ha:p1≠p2, which is a two-tailed test.

Step-by-step explanation:

We formulate our hypotheses as

H0:p1=p2; Ha:p1≠p2, which is a two-tailed test.

Supposing the probability or proportion of the first survey is equal to the probability or proportion of the second survey. This will be the null hypothesis and the alternative hypotheses would be that these two proportions or probabilities are unequal.

This is a two tailed test.

Answer:

an = 13*n

Step-by-step explanation:

Look the 40 term in the attached image

Answer: 520

Step-by-step explanation:

13x40=520

Answer:

y^2 = 2x + 6

2x = y^2 - 6

x = 1/2(y^2 - 6)

The points of intersection of the  curves are  calculated:

y + 1 = 1/2( y^2 - 6)

2y + 2 = y^2 - 6

y^2 - 2y - 8 = 0

( y - 4)(y + 2) = 0

y = 4, -2

when y = 4, x = 5 and when y = -2 x = -1.

Integrating between  y = 4 and y = -2

     4

     INT  [ ( y + 1 + 1/2 (6 - y^2) ]dy

     -2

=    4

    {   y^2 / 2 + y + 3y - y^3/6 }

 -2

= 13 1/3 - (-4 2/3)

13 1/3 + 4 2/3

= 18  answer.

Answer:

i think its 18.

Step-by-step explanation: