express: 4d divided by c + 3 ; when c=3 and d=6

When points x,y are chosen randomly from the intervals [0,2] and [0,1], respectively, the probability that y is less than or equal to x squared, i.e., y ≤ x², is 1/3.

To solve this problem, we need to determine the area of the region where y is less than or equal to x squared. We can visualize this region by graphing the equation y = x², which is a parabola that opens upward and passes through the points (0, 0) and (1, 1).

Next, we need to find the area of the rectangle formed by the intervals [0, 2] and [0, 1], which has an area of 2.

To find the probability that y ≤ x², we need to divide the area of the region where y is less than or equal to x squared by the area of the rectangle.

To do this, we can integrate the equation y = x² with respect to x from 0 to 1, which gives us the area under the curve between x = 0 and x = 1. This integral is equal to 1/3.

Therefore, the probability that y ≤ x² is 1/3.

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The percentage change of the population is P = 1.7 %

Given data ,

To calculate the percent increase from 2014 to 2015, we need to find the difference between the two population values, divide it by the initial value, and then multiply by 100 to get the percentage.

Population increase = 7,375 - 7,250 = 125

Percent increase = (Population increase / Initial population) * 100

Percent increase = (125 / 7,250) * 100 ≈ 1.7241

Rounding to the nearest tenth of a percent, the percent increase is approximately 1.7%.

Hence , the percentage change is P = 1.7 %

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4

Step-by-step explanation:

8/5(put 8 as numerator becuz we need to find all x from 5/8) x 2 1/2＝4

Answer:

f(x) = 72-12x

Step-by-step explanation:

this might be too late but it could be useful for future people

Answer:

f(x) = 72-12x

took a while to solve.......

The dimensions of the deck should be increased by 5 feet each

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

Length = 20 feet

Width = 25 feet

So, the area is

Area = 20 * 25

Evaluate

Area = 500

When increased by 50%, we have

(20 + x) *(25 + x) = 500 * 1.50

Evaluate

(20 + x) * (25 + x) = 750

Express 750 as 25 * 30

So, we have

(20 + x) * (25 + x) = 25 * 30

This means that

20 + x = 25

25 + x = 30

Solve for x

x = 5 and x = 5

This means that

Increment = 5

Hence, the lengths should be increased by 5 feet

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Answer:

  80a²b³c

Step-by-step explanation:

As with numbers, the LCM is the product of the highest-powered factors.

  16ab³ = 2⁴×a×b³

  5a²b² = 5×a²×b²

  20ac = 2²×5×a×c

The highest power of the factor 2 is 2⁴.

The highest power of the factor 5 is 5.

The highest power of the factor a is a².

The highest power of the factor b is b³.

The highest power of the factor c is c.

The LCM is 2⁴×5×a²×b³×c = 80a²b³c

Answer:

Step 4

Step-by-step explanation:

Jose's Steps are:

Step 1: Declare the variable:

Let x = the number of student signatures still needed.

Step 2: Create a ratio equivalent to:

\(\dfrac{\text{Total number of signatures needed}}{\text{Total number of students in the school}} =\dfrac{x + 82}{426}.\)

Step 3: Convert 25% to a decimal:

25% = 0.25.

Step 4: Write the inequality:

\(\dfrac{x + 82}{426}\leq 0.25\)

Since they need at least 25% of the student population to sign a petition, In Step 4, the inequality should be:

\(\dfrac{x + 82}{426}\geq 0.25\)

Answer:

(D).Step 4

Step-by-step explanation:

I got it right on edge

Given the function:

Let's find the minimum and maximum values over the interval [0, 2π].

Let's first find the derivative of the function:

Now set the derivative to 0 and solve for x:

The cosine function is positive in quadrants I and IV, to find the reference angle(minimum), subtract the first solution from 2π:

Plug in the values in the function to determine the minimum and maximum:

Therefore, we have the following:

Minimum occurs at: x = 3π/2

Maximum occurs at: x = π/2

ANSWER:

Answer:

5(9x+23)

Step-by-step explanation:

45x+115

5(9x+23)

The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.

To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.

Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.

y = -9x + b

Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:

-1 = -9(0) + b

-1 = b

Therefore, the y-intercept (b) of the perpendicular line is -1.

Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:

y = -9x - 1

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The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Answer:

C. I hope this helps! Have a great day.

Answer:

CCC

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

Herein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:

dy / dt = 3 · y · (1 - y / 14)

dy / [3 · y · (1 - y / 14)] = dt

dy / [- (3  / 14) · y · (y - 14)] = dt

By partial fractions we find the following expression:

- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt

- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.

y = 14 / [1 - C · tⁿ], where n = - 14² / 3.

If y(0) = 10, then the particular solution is:

y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

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Answer:

6

Step-by-step explanation:

From the odd-degree terms, take out one copy and rewrite the series as

\(1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x+5x^3+\cdots\)

\(1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x(1+x^2+\cdots)\)

Then if |x| < 1, we can condense this to

\(\displaystyle\sum_{n=0}^\infty x^n+5x\sum_{n=0}^\infty x^{2n}=\frac1{1-x}+\frac{5x}{1-x^2}=\frac{1+6x}{1-x^2}\)

Since the series we invoked here converge on -1 < x < 1, so does this one.

The explicit formula of the function f(x) is \(f(x) = \frac{1 + x + 5x}{1-x^2}\)

The function definition is given as:

\(f(x) = 1 + 6x + x^2 + 6x^3 + x^4 + ...\)

Expand the terms of the expression

\(f(x) = 1 + 5x + x + x^2 + 5x^3 + x^3 + x^4 + ...\)

Split

\(f(x) = (1 + x + x^2 +x^3 + .....) + 5x + 5x^3 + .. ...\)

Factor out 5x

\(f(x) = (1 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...\)

Express 1 as x^0

\(f(x) = (x^0 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...\)

Express x as x^1

\(f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...\)

Also, we have:

\(f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(x^0 + x^2) + .. ...\)

Rewrite the series using the summation symbol

\(f(x) = \sum\limits^{\infty}_{n=0}x^n+ 5x\sum\limits^{\infty}_{n=0}x^{2n}\)

The sum to infinity of a geometric progression is:

\(S_{\infty} = \frac{a}{1- r}\)

Where:

a represents the first term, and r represents the common ratio

Using the above formula, we have:

\(\sum\limits^{\infty}_{n=0}x^n = \frac{1}{1 - x}\)

\(5x\sum\limits^{\infty}_{n=0}x^{2n} = 5x * \frac{1}{1 - x^2} = \frac{5x}{1-x^2}\)

So, we have:

\(f(x) = \frac{1}{1-x}+ \frac{5x}{1-x^2}\)

Take the LCM

\(f(x) = \frac{1 + x + 5x}{1-x^2}\)

Evaluate the like terms

\(f(x) = \frac{1 + 6x}{1-x^2}\)

Hence, the explicit formula of the function f(x) is \(f(x) = \frac{1 + x + 5x}{1-x^2}\)

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The property illustrated ca be classified as the transitive property of equality

Equation are expressions separated by an equal sign. For transitive property, if two system of equation are equal, and the first is equal to the second, then they 2nd is equal to the third, they are transitive.

According to the transitive property of equality, two quantities that are equal to the same thing are equal to each other. For instance If x = 10 and 10 = y, then x = y.

Given that g = 3h and 3h = 16, then g = 16, then the property illustrated ca be classified as the transitive property of equality

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The new balance is a credit of $ 48.78.

Since Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%, and during the monthly billing cycle, Ben charged $ 238.75, made a payment of $ 300.00, and had a finance charge of $ 7.99, to find his new balance, the following calculations must be performed:

Therefore, the new balance is a credit of $ 48.78.

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Step-by-step explanation:

Team A time is    1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr

Team B =   1 / ( 1/3 + 1/3) =  1 1/2 hr

Team A wins !

Answer:

Answer is 7.

Step-by-step explanation:

(a + 2)^4- 20(a + 2)^2+ 64 = 0

2a^4- 20(2a)^2+ 64 = 0

16a-20(4a)+64=0  

-4a    -64  -4a          -64

12a-84=0

    +84 +84

12a=84

84/12=7

Answer:

\(\boxed {x = -1}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(15 + 3x = 3(2 - 2x)\)

-Use Distributive Property:

\(15 + 3x = 3(2 - 2x)\)

\(15 + 3x = 6 - 6x\)

-Take \(6x\) and add it to \(3x\):

\(15 + 3x + 6x = 6 + 6x - 6x\)

\(15 + 9x = 6\)

-Subtract both sides by \(15\):

\(15 - 15 + 9x = 6 - 15\)

\(9x = -9\)

-Divide both sides by \(9\):

\(\frac{9x}{9} = \frac{-9}{9}\)

\(\boxed {x = -1}\)

Therefore, the value of \(x\) is \(-1\).

Answer

18 and 54

Step-by-step explanation:

Answer:

The answer is 4√3 - 6

Steps

(8√6mn + 6√8mn ) / 2√2mn

Factor out 2√mn from the expression

That's

2√mn × ( 4√6 - 3√8) / 2√2mn

Next reduce the fraction with 2

We have

√mn × ( 4√6 - 3√8) / √2mn

Factor √2 from the denominator

√mn × ( 4√6 - 3√8) / √2(√mn)

√mn will cancel each other

we get

( 4√6 - 3√8) / √2

Simplify the radical expression

That's

( 4√6 - 3× 2√2) / √2

= ( 4√6 - 6√2) / √2

Rationalize the surd

We get

( 4√6 - 6√2) / √2 × (√2 / √2)

= ( 4√6 - 6√2) (√2) / (√2)²

= 4√12 - 12 / 2

= (8 √3 - 12) / 2

Factor out 2 from the numerator

That's

2( 4 √ 3 - 6 ) /2

2 will cancel each other

so the final answer will be

4√3 - 6

Hope this helps you

Answer:

300+ 80+6

Step-by-step explanation:

i think i not sure

Answer:

Wouldn't P be something less or equal to an acute angle? Try 75°.

Answer:

its 300∘ I got it right

Answer:

what is it

Step-by-step explanation:

what is it?

Answer:

Step-by-step explanation:

100000$

its CL i think im very sorry if im wrong

Answer:

Simplifying the expression `n + n - 0.18n`, we get:

n + n - 0.18n = 2n - 0.18n

Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.

Looking at the answer choices:

a. 1.18n

b. 1.82n

c. n- 0.18

d. 2n - 0.82

We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.

Therefore, the answer is d. 2n - 0.82.

Step-by-step explanation:

Answer:

A. |12| > √80

B. √53 > |-5.3|

Step-by-step explanation:

A.  |12| > √80

The absolute value of 12 is 12, and the square root of 80 is 8.9442. This means the number sentence is true because it states that the absolute value of 12 is greater than the square root of 8.

B. √53 > |-5.3|

The square root of 53 is 7.2801 and the absolute value of -5.3 is 5.3. This means the number sentence is true because is states that the square root of 53 is greater than the absolute value of -5.3

have a nice day!

5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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