Express \big(\frac{2}{3}x+3\big)^2(
3
2
​
x+3)
2
as a trinomial in simplest form.

Answer:

Step-by-step explanation:

Correct choice is D

Answer:

4√(5)

Step-by-step explanation:

√(20)-√(5)+√(45)

→ 2√(5)-√(5)+3√(5)

→ 4√(5)

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

There will be 16 possibilities for flipping the coin four times.

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

Given that, A two-sided coin has heads on one side and tails on the other side. flipped for four times.

We need to determine the sample space for flipping the coin four times.

Since, four coins are tossed, so the possibilities are either :-

HHHH or TTTT or HHHT or HHTH or

HTHH or THHH or HHTT or HTTH or

HTHT or THHT or THTH or TTHH or

HTTT or THTT or TTHT or TTTH

It means number of elements in sample space =

2⁴ = 16

Therefore, the sample space =

S = {HHHH, TTTT, HHHT, HHTH,

HTHH, THHH, HHTT, HTTH, HTHT,

THHT, THTH, TTHH, HTTT, THTT,

TTHT, TTTH}

Hence, there will be 16 possibilities for flipping the coin four times.

Learn more about sample space, click;

https://brainly.com/question/30206035

#SPJ1

The slope of a line that passe through the points (x1,y1) and (x2,y2) is given by:

From the graph we notice that the lines passes through the points (-1,1) and (3,-4); plugging the values of this points in the expression for the slope we have that:

Therefore the slope of the line is -5/4

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

The volume of the oblique cylinder is approximately 1,356.4 cubic units.

The formula for determining the volume of an oblique cylinder is expressed as;

V = πr²h

Where v is the volume of the oblique cylinder

r is the radius of the oblique cylinder

h is the height of the oblique cylinder

To find the volume of an oblique cylinder, we need its base area and its height.

Now, substitute the values into the formula

Volume, v = 3. 14 ×(6)² × 12

find the square of the value;

Volume, v = 3. 14 × 36× 12

Multiply the values

Volume, v = 1,356.4  cubic units

Therefore, the volume of the oblique cylinder is approximately 1,356.4  cubic units

Learn more about volume here:

brainly.com/question/1972490

#SPJ1

Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.

Divide the numerator (11) by the denominator (4).

11 ÷ 4 = 2 remainder 3

The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.

Write the mixed numeral using the whole number part and the fractional part.

The mixed numeral for 11/4 is:

2 and 3/4

Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

​for such more question on fraction

https://brainly.com/question/1622425

#SPJ8

Answer: 1400 is coffee.

Step-by-step explanation:

Answer:

I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion * 360° = 0.6 * 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.

Answer:

Whe we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here, so the domain is:

x ∈ (-∞, ∞)

Answer:

Yes I do it it’s just

Step-by-step explanation:

Why do I

Linear equations are typically organized in slope-intercept form:

\(y=mx+b\)

Perpendicular lines have slopes that are negative reciprocals.

We're given:

1) Determine the slope

Let's first rearrange this equation into slope-intercept form:

\(4x-5y=-10\\-5y=-4x-10\\\\y=\dfrac{4}{5}x+2\)

Notice how \(\dfrac{4}{5}\) is in the place of m in y = mx + b. This is the slope of the give line.

Since perpendicular lines are negative reciprocals, we know the slope of the other line is \(-\dfrac{5}{4}\). Plug this into y = mx + b:

\(y=-\dfrac{5}{4}x+b\)

2) Determine the y-intercept

We're also given that the line passes through (6,3). Plug this point into our equation and solve for b:

\(y=-\dfrac{5}{4}x+b\\\\3=-\dfrac{5}{4}(6)+b\\\\b=3+\dfrac{5}{4}(6)\\\\b=\dfrac{21}{2}\)

Plug this back into our original equation:

\(y=-\dfrac{5}{4}x+\dfrac{21}{2}\)

\(y=-\dfrac{5}{4}x+\dfrac{21}{2}\)

Answer: in the third draw 33.33% people eliminated.

Step-by-step explanation:

The  probability that all seniors will be chosen at random is 5/9.

We have,

Seniors = 5

Juniors = 4

Total number of people= 5 + 4 = 9

So, the probability that all seniors will be chosen at random is

= Number of senior/ total number of person

= 5 / 9

Thus, the required probability is 5/9.

Learn more about Probability here:

https://brainly.com/question/2430384

#SPJ1

a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

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

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

for such more question on secant slope

https://brainly.com/question/27877215

#SPJ8

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the equation 4 ⁢ x 2 − 16 ⁢ x + 8 = 0 by completing the square, we first divide both sides by 4 to get x^2 - 4x + 2 = 0.

Then we add (b/2)^2 to both sides of the equation where b is the coefficient of x. In this case, b = -4.

So we add (-4/2)^2 = 4 to both sides of the equation.

This gives us

x^2 - 4x + 6 = 4.

We can then write this as

(x - 2)^2 = 2.

Taking the square root of both sides gives us

x - 2 = ±√2.

Solving for x gives us

Answer: x= 2 -√2 and x = 2 ± √2

Step-by-step explanation:

Divide both sides of the equation by 4 to get x^2 - 4x + 2 = 0.

Move the constant term to the right side of the equation to get x^2 - 4x = -2.

Add the square of half of the coefficient of x to both sides of the equation to get x^2 - 4x + 4 = -2 + 4. This makes the left side a perfect square trinomial.

Factor the left side of the equation and simplify the right side to get (x - 2)^2 = 2.

Take the square root of both sides of the equation to get x - 2 = ±√2.

Add 2 to both sides of the equation to get x = 2 ±√2.

Therefore, the solutions are x = 2 +√2 and x = 2 -√2.

Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

To see more related questions follow the link:

https://brainly.com/question/30721594

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

Learn more about greatest common factor  at;

https://brainly.com/question/219464

#SPJ1

The domain is all real numbers and the range is greater than zero. Then the correct option is A.

Given that:

Function, y = 1/2 · (2)ˣ

The domain means all the possible values of x and the range means all the possible values of y.

The function is an exponential function, then the domain of the function will be all real numbers.

The value of the exponential function is always positive. Then the range will be greater than zero.

The domain is all real numbers and the range is greater than zero. Then the correct option is A.

More about the domain and range link is given below.

https://brainly.com/question/12208715

#SPJ1

Answer:

Step-by-step explanation:

If the wall is perpendicular, then that means that this is a right triangle. We can find out if it is by using Pythagorean's Theorem and filling in the values for the sides. If the statement is true, then the triangle is right and the wall is perpendicular to the base.

\(a^2+b^2=c^2\) and filling in:

\(7^2+8^2=12^2\) Let's find out if this is true:

\(49+64=144\) Is this true?

113 = 144

Definitely not true. So this is not a right triangle and the wall is not perpendicular to the floor.

Answer:

$ 6.20 Cents

Step-by-step explanation:

17 - 5.50= 11.5

11.50 - 5.30= 6.2

Add A Zero at the end

You Get 6.20

Answer:

410.77

Step-by-step explanation:

Hope this helps

Answer:

56, 59

Step-by-step explanation:

Looks like you just add 3 each time

Answer: The equation is skip counting by 3’s

the answer is 56, and 59

9514 1404 393

Answer:

  0.9114

Step-by-step explanation:

That multiplier would be ...

  (1 -2%)×(1 -7%)

  = (1 -0.02)(1 -0.07)

  = 0.98×0.93 = 0.9114

The volume of the cone is 144π units³.

The volume of a cone can be calculated as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore, the height of the cone is 27 units and the radius of the cone is given as 4 units.

Let's find the volume using the formula,

r = 4 units

h = 27 units

Therefore,

volume of a cone = 1 / 3 πr²h

volume of a cone = 1 / 3 × π × 4² × 27

volume of a cone = 1 / 3 × π × 16 × 27

volume of a cone = 432 / 3 π

Therefore,

volume of a cone = 144π

learn more on volume here:https://brainly.com/question/29767724

#SPJ1

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

For  more such questions on gross earning.

https://brainly.com/question/29206567

#SPJ8

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

Learn more about Probability here:

brainly.com/question/32117953

#SPJ1

The best unit of measurement for Alex to use for the ropes he is going to use at camp would be centimeters because it is a measurement that fits the needs of his knot shop.

A unit of measure is a unit that is used as a reference and international standard on length, weight, height, among others.

In the case of length, there are several units of measurement such as:

For a knot-making workshop in a camp, the ideal would be to have a rope of at least 2 or 3 meters. However, the ideal unit of measurement for teaching about knots is centimeters because knots do not require a large amount of rope to tie.

Learn more about knots in: https://brainly.com/question/15458643