The Roxbury CC Tigers basketball team scored 12 points in the first 6 minutes of a game. If they continue at the same pace, how much will they score during the entire 40 minute game?

Answer:

n > 8

Step-by-step explanation:

Let's call the unknown number n. Set up the inequality: (n-6)×4>n

Distribute on the left side, subtract the n from the right to the left, and continue solving.

Answer:

5 coffees will cost $9.25

Step-by-step explanation:

If you divide $5.55 by the 3 coffees, you get $1.85 which is the price per coffee. Multiply $1.85 by 5 to get $9.25 which is the cost for 5 coffees

Answer:

Option D: 8.19 inches

Step-by-step explanation:

i hope this helps..have a great day! :)

Answer: x=25/4 or 6.25, y=79/16 or 4.9375

Step-by-step explanation:

Normally, we would have to set up a system of linear equations, but in this case we can solve for x and plug in from there. x=5/2 or 2.5 when solving for the variable. Now we go to the second equation, plug for x, and solve for y. 5/2 times 5/2 is 25/4, multiplied by 3 is 75/4. Subtract 75/4 from -1, and divide both sides by -4.

Answer:

A fruit seller buys 712 fruits of which 3/4 are apples. The apples that he bought 1/3 were found to be rotten if he sold all the good apples at Rs.5 1/4 each.

Step-by-step explanation:

The total possible outcome when a coin is flipped and a die is rolled is 12

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total possible outcomes.

For example if a coin is flipped, a coin only has two faces, this means that it will have 2 Total possible outcome. When a die is rolled, a die has 6 faces which means that it will Total outcome of 6. When both a coin is flipped and a die is rolled the total possible outcome is 6×2 = 12 outcomes.

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Answer:

Step-by-step explanation:

from the figure we understand that it is an isosceles triangle, therefore 2 sides and two congruent angles, BD and CD are congruent, therefore 3x = x + 16.

let's solve

3x = x + 16

2x = 16

x = 8

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

check

3 × 8 = 8 + 16

24 = 24

thee answer is good

The percentage of card  which is not divisor of 45 is 23.077%

Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.

What does the term "percent" mean?

A fraction of one hundred is used to express a quantity or ratio as a percentage. The acronyms "pct," "pct," and occasionally "pc," as well as the percent symbol, "%," are also frequently used.

A % is a numeric expression that lacks both dimensions and a measurement system. The formula to determine the proportion of one number to another is percentage = (Original number/Another number) x 100.

In mathematics, a percentage is a number or ratio that represents a portion of 100. In percentages, 100% is meant. It contains no units.

A %, also known as a decimal or a fraction, is a figure that indicates how many out of 100 we are discussing. For example, "three for the price of one" is a percentage.

Given That:

In the deck of 52 cards You pick randomly 5 , 6 , 7 , 8
so each card has 4 variant
now for getting probability of not getting a divisor of 45 is
total outcomes = 52
observable outcomes = 4+4+4 = 12
its because 5 is a divisor so we didn't include it
hence the probability is 12/52
Percentage of this probability is 0.23077 x 100 = 23.077%

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The division of negative 7 and 4 over 7 ÷ negative 8 and 1 over 5 is A. 265 over 287

A division simply shows the separation of the number that is given. It should be noted that division is illustrated by the symbol / or ÷.

In this case, negative 7 and 4 over 7 ÷ negative 8 and 1 over 5 will be:

= (- 7 4/7) ÷ (- 8 1/5)

= - 53/7 ÷ (-41 / 5)

= -53/7 × -5/41

= 265 / 287

Therefore the correct option is A.

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Answer: 265/287

I'm not an average brain like other people.

The exchange rate of US dollars per Australian dollar is 0.72

The exchange rate of Australian dollars per US dollar is 1.39

Exchange rate

Exchange rate is the price of a country's money in relation to another country's money and it is “fixed” when countries use gold or another agreed-upon standard, and each currency is worth a specific measure of the metal or other standard.

Given,

After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian dollars. Complete the two statements based on this currency exchange.

Here we need to find the exchange rate of US dollars per Australian dollar and Australian dollars per US dollar then round it to the nearest hundredth.

According to the given details,

Total amount in US dollars = $750

Converted amount in Australian dollar = $1,041.67

When we divide the US dollar by the Australian dollar then we get the value of one dollar rate,

=> 750/1041.67

=> 0.719

When we round off it to the nearest hundredth then we get the exchange rate of $1 is 0.72

Similarly, now we have to divide the Australian dollar by the US dollar then we get the value of one dollar rate,

=>  1041.67/750

=> 1.388

When we round off it to the nearest hundredth then we get the exchange rate of $1 is 1.39.

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The formula for the perimeter of the rectangle is:

P(x) = 14x - 16

We know that for a rectangle of length L and width W the perimeter is given by the formula:

P = 2*(W + L)

In this case we know that:

W = 2x - 1

L = 5x - 7

Replacing that in the perimeter formula we get:

P(x) = 2*(2x - 1 + 5x - 7)

Now we can simplify this so we get:

P(x) = 2*(2x + 5x - 1 - 7)

P(x) = 2*(7x - 8)

P(x) = 14x - 16

That is the perimeter of the rectangle in terms of x.

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With a manufacturing cost of $80 per phone, the selling price of $292.5 would result in the largest annual profit.

Profit is the amount of gain realized from a transaction. The profit formula is useful for figuring out the profit from selling a specific product, typically in a business, or for figuring out the gain in any financial transaction. If the selling price is more than the cost price, a profit can be determined.

Given,

q = -6p+3030

p = 505 - q/6

R(q) = 505q - q²/6

C(q) = 80q

Now, the profit function,

P(q) = R(q) - C(q)

      = (505q - (q²/6)) - 80q

P(q) = 425q - q²/6

P(q) = 425 - q/3

q = 1275 units

Now, put it in the demand function,

p = 505 - q/6

  = 505 - 212.5

  = 292.5

Therefore, the selling price is $292.5.

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By the concept of polynomial, first second and third option are correct.\

What is polynomial?

At first it is important to know about algebraic expression

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

An algebraic expression of the form [tex]a_0+a_1x+a_2x^2 + ....+a_nx^n[/tex] is called a polynomial of degree n

For the First Option

5 - 2a is in the form of [tex]b_0 + a_1a[/tex]

So the first option is a polynomial

For the second option

[tex]4 - 8^2 -16\\4 -64 -16\\-76[/tex]

which is a constant

And all constants are polynomial

So the second option is a polynomial

For the third option

[tex]5x^3 +4x^13x +1\\5x^3 + 12x^2 +1[/tex]

which is of the form [tex]a_0+a_1x + a_2x^2 + a_3x^3, a_1 = 0[/tex]

So the third option is a polynomial

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The equation of the perpendicular bisector for the line is y = 1/3(x) - 2

Given: the endpoints of the line (4,6) and (8,-6)

The bisector of the line will divide the line into two i.e. the bisector will be at the point of the line.

The coordinate of the midpoint can be calculated using the formula below:

Xm = (X1 +X2)/2  and Ym = (Y1 +Y2)/2

Where X1 = 4, Y1 =6 and X2= 8, Y2= -6

Xm = (4+8)/ 2 = 12/2 = 6  and Ym = (6+(-6))/2 = 0/2 = 0

Thus, midpoint(6, 0)

slope  = y2-y1 / x2-x1

Thus, the slope of the line segment (m₁)  = -6-6 / 8-4 = -12/4 = -3

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ × m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the bisector be  m₂

-3 × m₂ = -1

m₂ = 1/3

Equation of perpendicular bisector with coordinate (6,0):

y - 0 = 1/3(x-6)

y = 1/3(x-6)

y = 1/3(x) - 2

Therefore, the equation for the perpendicular bisector of the line segment is y = 1/3(x) - 2

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The terms which are equivalent to the slope in a proportional relationship include:

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope formula is the rise over run formula, where the fraction consists of a rise, whether the line is going up or down, divided by the run.

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Complete question

Select all the terms which are equivalent to the slope in a proportional relationship.

Constant of proportionality

Origin

Inverse

Rise over run

Unit rate

Answer:

The correct answer is D

Step-by-step explanation:

the negative power shows that on the exponent shows that the value is small and is being simplified.

When ever there is a negative power we increase zeros with respect to the exponent value.

Answer:

$93.75

Step-by-step explanation:

$125 × 0.75 = $93.75

Answer:

$93.75

Step-by-step explanation:

125x0.25

31.25

125-31.25

$93.75

Hopes this helps

Regarding the given matrix, it is found that:

1. a. The matrix has three rows.

1. b. The matrix has five columns.

1. c. The matrix has two dimensions.

2. The entry is 2.

3. The entry is 7.

4. The entry is -2.

5. The entry is 0.

6. The entries are: m21 and m33.

The matrix is composed by three lines of elements, and each line has five elements, hence:

The number of dimensions of the matrix are:

2, which are the rows and the columns.

The entries are symbolized as follows:

mrc.

In which:

Hence the entry m11, for example, is the element at the first row and at the first column, which is of 2.

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The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

According to the question,

We have the following information:

Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.

We know that the following formula is used to find the area of rectangle:

Length*width = 18

Length*3 = 18

Length = 18/3

Length of the rectangular garden = 6 meters

Now, perimeter of the rectangular garden:

2(length+width)

2(6+3)

2*9

18 meters

Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

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Answer:

28, -27, 108, -42

Step-by-step explanation:

when x=2, 11x+6 = 22+6=28,

2x+28x+48= 30x+48=60+48=108

when x=-3, 11x+6 = -33+6=-27,

2x+28x+48= 30x+48=-90+48=-42

Answer:

I got 28, -27, 108, and -42. See explanation for the answer for which problems

Step-by-step explanation:

11x + 6 = ?

2x + 28x + 48 = ?

x = 2 and x = -3

Let's start with the first equation

Using x = 2

11(2) + 6 = ?

22 + 6 = 28

Using x = -3

11(-3) + 6 =?

-33 + 6 = -27

Second equation

Using x = 2

2(2) + 28(2) + 48 = ?

4 + 56 + 48 = 108

Using x = -3

2(-3) + 28(-3) + 48 = ?

-6 - 84 + 48 = -42

The statements that are true about the ordered pair (−4, 0) and the system of equations include the following:

In order to determine which statements are true with respect to a solution of the given system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (-4, 0), we have:

2x + y = -8x

2(-4) + 0 = -8(4)

-8 = -32 (False)

For ordered pair (-4, 0), we have:

x - y = -4

-4 - 0 = -4

-4 = -4 (True).

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After 16.9 years the population will reach to 24300.

What do you mean by exponential growth and decay?

Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously. Studying bacterial growth, population expansion, and money growth schemes all use exponential growth.

It is given that a town has a population of 16000 and grows at 2.5% every year.

Now we need to  find the time period when the population will reach 24300

So, [tex]24300 = 16000(1+0.025)^{t}[/tex]

24300/16000 = [tex](1+0.025)^{t}[/tex]

24300/16000 = [tex]1.025^{t}[/tex]

1.51875 = [tex]1.025^{t}[/tex]

Taking log on both sides we get,

log(1.51875) = t log(1.025)

0.18148 = t (0.01072)

t = 0.18148/0.01072 = 16.9

Therefore, after 16.9 years the population will reach to 24300.

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Answer:

(4)

Step-by-step explanation:

Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.

Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x

Then, since the result of this is four more than the smaller, this expression is x+4.

Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.

Hence, the option (4) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.

Let us assume the smaller number is [tex]x[/tex].

The larger number is  [tex](x+2)[/tex].

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is

[tex]3(x+2)-2x[/tex]

So, the result is four more than the smaller.

i.e., [tex]3(x+2)-2x=x+4[/tex]

Hence, the option (4) is correct.

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Answer:

the graphical explanation please

Answer:

a) -2/3

b) x^2-1/2

Step-by-step explanation:

The complete table of values of the function is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

The ordered pairs are (x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

The equation of the function is given as

f(x) = 2ˣ

On the incomplete table of values, we have the following x values

x = 0, 1, 2, 3

Next, we substitute x = 0, 1, 2, 3 in the equation f(x) = 2ˣ

So, we have:

f(0) = 2⁰ = 1

f(1) = 2¹ = 2

f(2) = 2² = 4

f(2) = 2³ = 8

So, the complete table is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

When represented as ordered pairs, we have

(x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

See attachment for the graph

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The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

Given,

In the question:

The function is:
f(x) =  [tex]x^4(5x^4+4)[/tex]

Differentiate the function with respect to x.

Now, According to the question:

f(x) = [tex]x^4(5x^4+4)[/tex]

Expand the expression:

f(x) = [tex]5x^8+4x^4[/tex]

Calculate the derivative

f'(x) =  [tex]\frac{d}{dx}(5x^8+4x^4)[/tex]

f'(x) = [tex]\frac{d}{dx}(5x^8)+\frac{d}{dx} (4x^4)[/tex]

Isolate Coefficients

f'(x) = 5 x [tex]\frac{d}{dx}(x^8)+4 \frac{d}{dx} (x^4)[/tex]

Apply the power rule

f'(x) = 5x [tex]8x^7+4[/tex] x[tex]4x^3[/tex]

f'(x) = [tex]40x^7 + 16x^3[/tex]

Hence, The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

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Answer:

The probability is 81%

Step-by-step explanation: