1. Pemba attempted 25 free throws. She made 12 of them and missed 13.
Show her free-throw results as a fraction. Explain why a fraction is a
useful way to show these statistics.

The domain of the function 5h + 2d = 15 is [0, 3].

What is domain and range of a function?

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x).

                           The collection of numbers that the function assumes is known as its range. The values that the function outputs when we enter an x value are in this set.

5h + 2d = 15

2d = 15 - 5h

d = (15 - 5h)/2

For h = 0, d = 15/2 = 7.5

For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.

For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.

For h = 3, d = (15 - 15)/2 = 0 miles

The domain of the function is [0, 3].

Thus,

The domain is [0, 3].

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Answer: c

Step-by-step explanation:

-3v - 2v > 35

combine like terms: -5v > 35

divde by the same term (isolate the variable): -5v/-5 , 35/-5

v < -7

Using the concept of multiplication and division, the number of chocolate sold each month is 400 packs.

To determine the number of chocolate biscuits in the shop, we have to determine how many is contained in each box and then multiply it by number of days in a month and then subtract the number of chocolate in the shop. This tasks involves the use of basic arithmetic operations to determine the number of packs sold.

The total number of packs of biscuits in the shop was 160 * 30 = 4800.

So, the number of packs of chocolate biscuits was 4800 - 2800 = 2000.

The shopkeeper sold 2000 packs of chocolate biscuits over 5 months, so he sold 2000 / 5 which will give us 400 packs of chocolate biscuits each month.

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Explanation:

The two horizontal sides are parallel. The side marked 34 is half as long as side x.

In other words, side x is twice as long as the side marked 34.

x = 2*34 = 68

For more information, search out "midsegment of a triangle".

The function which models the data as represented on the graph will be; [tex]f(x) = 0.8(1/2)^x[/tex].

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

The given graph is an exponential function and should take the form;

[tex]f (x) = a (b)^x[/tex]

Hence, using values from the graph;

For ( -1, 0.2 ) = a • b..........(i)

For (0, 0.8); 10.5 = a • b².........(ii)

=> x=0 and y= 0.8

So.

0.8=a(1/2)^0

0.8=a

Thus, the rule for the function is; y=0.8(1/2)^x

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Using the properties of sets, (BU A)'n C = {h,q}

Null set or an empty set There isn't even one element in it. Finite Set: It only has a finite number of components. The element count of an infinite set is infinite. Two sets with the same members are said to be equal sets.

An object collection that is taken into account as a whole is referred to as a set. The elements or members of the set are the things that make it up. A set's components can be any type of object, but for our purposes, they are most frequently mathematical components like integers, functions, or other sets.

The list of all subsets of a,b,c,d is ϕ ,{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}

(B U A) = {f,g,r,x,y,z}

(BU A)'n C = {h,q}

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After simplification, the value of expression is, (x + 1) / (2x - 1).

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The expression is,

⇒ 10x² + 10x / 20x² - 10x

Now, We can simplify as;

⇒ (10x² + 10x) / (20x² - 10x)

⇒ 10x (x + 1) / 10x (2x - 1)

⇒ (x + 1) / (2x - 1)

Thus, The value of expression is, (x + 1) / (2x - 1).

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Answer:15

Step-by-step explanation:

i did the math

Answer:

15

Step-by-step explanation:

15 x 2=30

15x3=45

The solution satisfying y1(0)=14 and y2(0)=-3 are y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13))) and y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))

The logistic equation is a non-linear ordinary differential equation that models the growth of populations over time.

The solution to the logistic equation with initial conditions y1(0)=14 and y2(0)=-3 is given by (from a graphing tool):

y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13)))

y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))

Note: ln is the natural logarithm function.

The time t when y1(t)=7 can be found by solving for t in the equation y1(t) = 7.

From the graphing tool, we have

t = 1.08 when y1(t) = 7

he solution y2(t) becomes infinite when the denominator of the equation becomes zero.

This occurs when -3/2 * e^(t * ln(-3/2)) = -∞.

This can be written as t * ln(-3/2) = ∞, which occurs when t approaches positive infinity.

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Answer: The perimeter triples.

Step-by-step explanation:

Since there is a direct variation, if the side length triples, so does the perimeter.

Answer:

It's the third choice.

Step-by-step explanation:

IF y varies inversely as x then y = k/x   where k is a constant,

and k = xy    

For the 3rd choice

-1 * -2/7 = 2/7

4 * 1/14 = 2/7 and

6 * 1/21 = 2/7

so, this is inverse variation.

The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.

Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per​ hour, with a standard deviation of 4 miles per hour.

[tex]\mu = 64[/tex] and [tex]\sigma = 4[/tex].

Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.

Therefore, 75% of the vehicles would fall into this category.

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The rate of change of the hypotenuse is given as follows:

dh/dt = 2 in/sec.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The hypotenuse is then given as follows:

h² = x² + y².

For this problem, the hypotenuse has the value given as follows:

h² = 33² + 44²

h = square root(33² + 44²)

h = 55.

Applying implicit differentiation, the rate of change of the hypotenuse is obtained by the equation as follows:

h dh/dt = x dx/dt + y dy/dt.

Replacing the values, the rate of change is calculated as follows:

55dh/dt = 33 x 10 - 44 x 10

55dh/dt = -110

dh/dt = -110/55

dh/dt = 2 in/sec.

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The following mathematical expression matched with its translation:

1. x + y = 6 (the sum of two numbers is six)

2. x + y (the sum of x and y)

3. xy (the product of two numbers)

4. x ÷ y (x divided by y)

5. y ÷ x (y divided by x)

6. y = x - 6 (six less than a number is y)

7. x - y (x minus y)

8. 6 x = y (six times a number equals y)

9. xy = 6 (the product of two numbers is six)

10. y - x (x subtracted from y)

Mathematical expression can be translated as thus;

the sum of two numbers is six

Let the unknown numbers be x and y respectively

So,

x + y = 6

six less than a number is y

x - 6 = y

also written as

y = x - 6

six times a number equals y

6 × x = y

6x = y

also written as

y = 6x

Therefore, mathematical expressions are algebraic representation of mathematics in words.

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Step-by-step explanation:

Let's call the time it took Pat and Rich to drive to the beach "x".

The time it took them to drive back was twice as long, so it took 2x hours.

The total time spent traveling was x + 2x = 3x hours.

Since they spent 9 hours traveling, 3x = 9 hours.

So, x = 9 hours / 3 = 3 hours.

This means it took Pat and Rich 3 hours to drive to the beach and 2 * 3 = 6 hours to drive back.

Mr. Lopez cover in sand by 50 yd².

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Mr. Lopez is looking to fill a part of a park with sand.

And, The shape below represents the part of the park being covered in sand.

Now, We will find the area of figure as;

The park is mix of two figure rectangle and triangle.

Hence, We get;

Area of rectangle = 5 × 8

                           = 40 yd²

And, Area of triangle = 1/2 × 4 × 5

                                 = 10 yd²

Thus, The area of given figure is,

⇒ Area = 40 yd² + 10 yd²

⇒ Area = 50 yd²

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As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.

By dividing initial principal by the risk premium, the time it has been and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the technique used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating this is as a portion of the principal amount. For example, if he borrowed $100 from a buddy and agrees to pay back the loan at 5% interest, he will just pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must lend money when you lend it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.

given

Assuming a specific interest rate (r), principal (p), and number of times the interest is compounded annually (n), we can calculate the total amount owed on a loan (A) as follows:

A = p(1+ r/n) nl

Because in our example, n = 12 (monthly), p = $43,000, r = 2.4% = = 0.024, and t = 20 years.

A = $69457.89.

$289.41 per month for a 20-year term.

As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.

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The number of students who got actually enrolled are, 5400

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, a large university accepts ​60% of the students who apply. Of the students the university​ accepts, ​45% actually enroll, there are 20,000 students​ apply,

Since, the students whose application has been accepted = 20000 × 60%

= 12000

Now, the students who got admission = 12000 × 45%

= 5400

Hence, the number of students who got actually enrolled are, 5400

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The statement “Every sample space S is a finite set” is false because some sample spaces can be infinite, such as rolling a continuous random variable.

The statement “Every sample space S is a finite set” is false. A sample space is the set of all possible outcomes of a random experiment. While some sample spaces may be finite, not all sample spaces are. There are situations where the sample space can be infinite, such as when rolling a continuous random variable like a dice.

For example, the sample space of rolling a fair six-sided die is finite, consisting of the numbers {1, 2, 3, 4, 5, 6}. However, the sample space of choosing a real number between 0 and 1 is infinite, as there are infinitely many possible outcomes between 0 and 1.

Therefore, it is incorrect to say that every sample space is a finite set.

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Answer:

1225 is what I got, not sure tho.

The total area of all the pieces would be: -  x² + y² + 2xy = (x + y)².

This tile collection is composed of four tiles: two squares, each with sides of length x, and two rectangles, each with sides of length x and y.

The total area of all of the pieces can be expressed algebraically as A = x² + 2xy.

This expression can also be written as A = x² + xy + xy.

This tile collection is an example of a two-dimensional shape composed of two squares and two rectangles.

By adding the areas of each of these shapes, we can calculate the total area of the tile collection.

The area of each square is x², and the area of each rectangle is xy.

Adding these three expressions together gives us the total area, A = x² + 2xy.

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Answer:

1/2 bucket

Step-by-step explanation:

Each of the 8 buckets is 1/4 full.

The total amount of paint at the beginning is 8 × 1/4 bucket = 2 buckets.

Each student uses 1/4 of his paint. Combined, they use 1/4 of the total amount of paint in the buckets.

1/4 × 2 buckets = 1/2 bucket

Answer: 1/2 bucket

Answer:

The possible numbers of players are multiples of 6 (6, 12, 18, etc.).

Step-by-step explanation:

For the coach to be able to form teams of 6 players each, the total number of players must be divisible by 6. This means that if there are 6, 12, 18, 24, 30, etc. players, the coach can divide them evenly into teams of 6. Any other number of players would result in either having a team with more or fewer than 6 players, or leaving some players out. Hence, the possible numbers of players are multiples of 6.

The quadratic regression equation is y = 1.38x^2 - 5.77x + 0.96

From the question, we have the following parameters that can be used in our computation:

(-1,8), (5,-4), (7,8), (2,-6)

Using a graphing calculator, we have the following summary:

function value

mean of x 3.25

mean of y 1.5

correlation coefficient r 0.9990171837

A 1.380577428

B -5.769028871

C 0.9553805774

The equation is represented as

y = ax^2 + bx + c

So,, we habe

y = 1.38x^2 - 5.77x + 0.96

Hence, the equation is y = 1.38x^2 - 5.77x + 0.96

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Answer:

There are 0

Step-by-step explanation:

Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true

Answer:

A 0

Step-by-step explanation:

There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.

If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.

Answer:

y = 5x

where

y = number of fence posts that Edwin installs
x = number of hours that Edwin takes to install y posts

Step-by-step explanation:

Let y = number of fence posts that Edwin installs in x hours

We have the relation:

y ∝ x where ∝ is the symbol for is-proportional-to

We can rewrite this as an equation using the constant of proportionality,k:

y =kx

Given y = 40 fences, x = 8 hours we get

40 = k(8) = 8k

or, switching sides

8k = 40

k = 40/8 = 5

So Edwin can install 5 fences per hour

Plugging this into the equation of proportionality

y = 5x

The correct answer is A: 600 <= money <= 2822.4.

This represents the range of possible values that Pankaj's accumulated money could fall into, given the specified conditions of the 3% interest rate compounded weekly for a maximum of 2 years. The lower bound, 600, represents the initial deposit amount, while the upper bound, 2822.4, represents the maximum amount of money Pankaj could earn after 2 years, assuming that interest is compounded every week.

The experimental probability that the team made a goal on any given shot is 0.0625

From the question, we have the following parameters that can be used in our computation:

A soccer team made 2 goals out of 32 attempts in a game

The experimental probability that the team made a goal on any given shot is calculated as:

P = 2/32

Evaluate the quotient

P = 0.0625

Hence, the probability is 0.0625

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The domain of the function is given as follows:

[-10,10].

The domain of a function is the set containing all the input values of the function.

Hence, on the graph, the domain of the function is composed by the values of x of the function, and is given as follows:

[-10,10]. (closed due to the closed circle).

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