Which measurement represents the largest volume?

A) 999mL
B) .99L
C) 998cm³
D) 1.02L

Answer:

C = 81.6 degrees

Step-by-step explanation:

The formula for law of sines

sin A       sin B          sin C

--------  = -----------  = -------------

a                  b               c

Looking at the diagram,  we know A = 54, b = 7.4 and c = 15.8

not enough to use the law of sines

We will need to use the law of cosines

a^2 = b^2 + c^2 - 2ac cos A

Using the law of cosines, we can calculate the length of a

a^2 = 7.4^2 + 15.8^ -2*7.4*15.8 cos 54

a^2 = 54.6+249.64-233.84cos54

a^2 =166.7922966

a = 12.921

Now we can use the law of sines to find C

sin 54      sin C

--------  =  -------------

12.921           15.8

Using cross products

15.8 * sin 54 = 12.921 * sin C

Divide each side by 12.921

15.8 /12.921 * sin 54  = sin C

Take the arcsin of each side

arcsin (15.8 /12.921 * sin 54)  = arcsin (sin C)

arcsin (15.8 /12.921 * sin 54)  = C

C = 81.6 degrees

Answer:

The answer is 63/10, 63/100, 63/1000

Answer:

it would be SSS...

Step-by-step explanation:

Its meaning is "side side side''... so you see how the triangle, ABD has the dashed (same number of lines) through the lines of the triangle, it means the sides are all congruent meaning that the sides are the same

Answer:

The triangles are not congruent.

Step-by-step explanation:

The triangle ABD is an equilateral triangle, then all their sides are equal and all the angles are equal to 60º. Then x=60º and y=30º (because the sum of the internal angles of a triangle have to be 180º)

Then we can conclude that the triangles are not congruent because they share two sides, but does no have any angle in common, as we can see in the next list of the angles.

angle ADB= angle ABD= angle DAB=60º

angle BDC=30º

angle DCB=30º

angle CBD=120º

Answer:

sec theta = r/v

Step-by-step explanation:

sec theta  = 1 /  sin theta

We know that sin theta = opp/ hypotenuse

1 / sin theta = hypotenuse /  opp

sec theta = hypotenuse /  opp

sec theta = r/v

Answer:

Step-by-step explanation:

The edge length (s) of an equilateral triangle is (2/3)√3 times the height. This means the edge length of your triangle is ...

... s = (2/3)√3 × 12√2 = 8√6

The perimeter is 3 times the side length:

... p = 3s = 3×8√6 = 24√6 . . . cm

The area is half the product of edge length and height:

... a = (1/2)sh = (1/2)(8√6)(12√2) = 48√12 = 96√3 . . . cm²

The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².

To find the perimeter and area of an equilateral triangle with a given height, we can follow these steps:

First, let's denote the side length of the equilateral triangle as a. In an equilateral triangle, the height (h) can be found using the formula:

h = (a√3)/2

We know the height is 12√2 cm. Therefore,12√2 = (a√3)/2

To find the side length a, we can rearrange the equation: a = 2 * 12√2 / √3

Simplify the expression: a = 24√2 / √3

Multiplying numerator and denominator by √3 to rationalize the denominator: a = 24√6 / 3

a = 8√6

Now, the perimeter (P) of the equilateral triangle is given by: P = 3a

Substitute the value of a: P = 3 * 8√6

P = 24√6 cm

Next, we calculate the area (A) using the formula: A = (base * height) / 2

In an equilateral triangle, the base is equal to the side length a, and the height is given as 12√2 cm:

A = (8√6 * 12√2) / 2

Multiplying the bases and simplifying: A = (96√12) / 2

Since √12 can be simplified to 2√3: A = (96 * 2√3) / 2

A = 96√3 cm²

The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².

Answer:6: 8.64

7: 584

Step-by-step explanation:

48×.18=8.64

800×.73=584

Hope this helps

Answer:

Answer for question number 7 is 58.4

Step-by-step explanation:

Answer:

Same side: 4, 1.5, 5/3, 0.2

Opposite side: -5, -1/4

Step-by-step explanation:

We know that dilation caused by a positive factor leads to the object being on the same side and dilation caused by a negative factor leads to the object being on the opposite side. Therefore, the dilation caused by positive numbers 4, 1.5, 5/3, 0.2 will lead to object being on the same side. And dilation caused by a negative numbers -5 and -1/4 will lead to object being reflected to the opposite side

Answer:

38.4

Step-by-step explanation:

48*20%=9.6 48-9.6=38.4

Answer:

6

Step-by-step explanation:

f(x) = 3x - 1

f(2) means evaluate  f(x) when x=2

f(2) = 3(2) -1

f(2) = 6-1=5

g(5) means evaluate g(x) when x=5

g(5) = -5+6

g(5) =1

f(-2) + g(5)

5+1

6

Answer:

6

Step-by-step explanation:

Answer: 2x^3 - 7x^2 + 6x - 9 which is choice D

=========================================

Work Shown:

One way is to use the distribution rule two times

(x-3)(2x^2-x+3) = y(2x^2-x+3) ........... replace (x-3) with y

(x-3)(2x^2-x+3) = y(2x^2)+y(-x)+y(3) .... distribution rule

(x-3)(2x^2-x+3) = 2x^2*(y) - x(y) + 3(y)

(x-3)(2x^2-x+3) = 2x^2*(x-3) - x(x-3) + 3(x-3) .... replace y with x-3

(x-3)(2x^2-x+3) = 2x^3-6x^2 - x^2 + 3x + 3x - 9 ... distribution rule

(x-3)(2x^2-x+3) = 2x^3 - 7x^2 + 6x - 9

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

Or we can use the box method (see the attached image below). This is a visual way to organize the terms. You'll probably notice that the box method is basically the distribution rule. Each row is one distribution being applied. In row 1, we have x distributed to (2x^2-x+3). In row 2, we have -3 distributed to (2x^2-x+3). I color coded the table cells to highlight the like terms. Those like terms combine to -6x^2-x^2 = -7x^2 and 3x+3x = 6x as shown in the steps for the distribution above.

Each interior cell in the box is found by multiplying the corresponding outer terms. For example, in the first row, first column we have x^3 which is the result of multiplying the outer x and x^2 terms.

The correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

To find the product[tex]\((x - 3)(2x^2 - x + 3)\)[/tex], we can use the distributive property:

[tex]\((x - 3)(2x^2 - x + 3) = x(2x^2 - x + 3) - 3(2x^2 - x + 3)\)[/tex]

Now, distribute the terms:

[tex]\[= x \cdot 2x^2 - x^2 + 3x - 3 \cdot 2x^2 + 3x - 9\][/tex]

Combine like terms:

[tex]\[= 2x^3 - x^2 + 6x - 6x^2 + 6x - 9\][/tex]

Combine the x terms:

[tex]\[= 2x^3 - 7x^2 + 6x - 9\][/tex]

Therefore, the expression [tex]\((x - 3)(2x^2 - x + 3)\)[/tex]  is equal to \[tex](2x^3 - 7x^2 + 6x - 9\)[/tex].

So, the correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

Answer:

(-4,1)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

10 ways, 6th row

Step-by-step explanation:

You will flip a coin five times and get three heads and two tails. You can get it in

[tex]C_5^3=\dfrac{5!}{3!(5-3)!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot1\cdot 2}=10[/tex]

different ways.

6th row tells her the number of favorable outcomes for this event.

Answer: 3

Step-by-step explanation:

The slope of a line passing through two points (a,b) and (c,d) is given by :-

[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]

In the given graph , the line is passing through (0,0) and (1,3) .\

Then the slope of line  passing through (0,0) and (1,3) will be :-

[tex]\text{Slope}=\dfrac{3-0}{1-0}\\\\\Rightarrow\ \text{Slope}=3[/tex]

Hence, the slope of the given line= 3

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is that x = 19 is the solution because 3 * 19 - 15 = 57 - 15 = 42.

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is the option: x = 19 is not the solution because 3 * 19 - 15 = 3 * 4 = 12, not 42.

To check if a value is the solution to an equation, we substitute the value into the equation and perform the necessary calculations. In this case, substituting x = 19 into the equation 42 = 3x - 15 gives us 42 = 3 * 19 - 15 = 57 - 15 = 42. Since both sides of the equation are equal, x = 19 is indeed the solution.

The question is asking to determine if x = 19 is the solution for the equation 42 = 3x – 15. To verify this, we need to substitute x = 19 into the equation. So, we have 42 = 3(19) - 15 which simplifies to 42 = 57 - 15. After subtraction on the right side, we get 42 = 42, which is a true statement. Hence, x = 19 is indeed the solution to the equation 42 = 3x – 15.

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Final answer:

To find the scaled length of a line representing 5 feet on a scale drawing with a scale of 0.5 inches = 2 feet, set up a proportion and solve for x. The answer is 1.25 inches.

Explanation:

To calculate the length of a line on a scale drawing, you must use the scale provided and set up a proportion based on that scale. In this case, the scale is 0.5 inches = 2 feet. To find out what 5 feet would be on the drawing, we can set up a proportion where 0.5 inches/2 feet equals x inches/5 feet. Solving for x gives us:

0.5 inches / 2 feet = x inches / 5 feet

To keep the units consistent, we use cross-multiplication:

(0.5 inches) * 5 feet = 2 feet * x inches

2.5 inches = 2 feet * x inches

Now, divide both sides by 2 feet to solve for x:

x = 2.5 inches / 2 feet

x = 1.25 inches

Therefore, a line that represents an actual length of 5 feet would be 1.25 inches long on the scale drawing.

Answer:

The cannonball will hit the ground after about 5.926 seconds.

Step-by-step explanation:

h(t) = -4.9t² + 27.5t + 9.1

If you graphed the function on a graph, the cannonball would be hitting the ground when the function crossed the x-axis at 0. So, to solve this arithmetically, you just need to set h(t) equal to 0.

-4.9t² + 27.5t + 9.1 = 0   Plug this into a calculator if you have one, if not solve with the quadratic formula.

[tex]\frac{-27.5 \pm \sqrt{(27.5^2) - 4(-4.9)(9.1)} }{2(-4.9)}[/tex]

t = -.0313

t = 5.9256

Since time can't be negative, you know your answer will be 5.926 seconds.

Answer:

t =5.93 seconds

Step-by-step explanation:

h(t) represents the height of the cannon ball.  Zero is when the ball will hit the ground.    Substitute zero for h(t).

0 = -4.9t² + 27.5t + 9.1

This is a complicated quadratics, so we will need to use the quadratic formula to solve

-b ± sqrt(b^2 -4ac)

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

  2a

where a = -4.9   b = 27.5   and c = 9.1

-27.5  ± sqrt(27.5 ^2 -4 (-4.9) 9.1)

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

  2(-4.9)

-27.5  ± sqrt(756.25 +178.36)

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

  -9.8

-27.5  ± sqrt(943.61)

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

  -9.8

-27.5  ± 30.57139186

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

  -9.8

3.071391856/-9.8   or  -58.07139186/-9.8

-.313407332  or  5.925652231

But time cannot be negative,  the ball cannot land before it takes off,

so t= 5.925652231 seconds

Rounding to the nearest hundredth

t =5.93 seconds

Answer:

600kW

Step-by-step explanation:

Referring to the fact that 10m/s of wind is 500kW so divide 500 by 10.

500/10=50

So there is 50 kW is 1m/s of wind. Now multiply 12 by 50

12x50=600

So for 12m/s of wind there is 600kW

At 12 m/s, the turbine generates 864 kW.

We can express the given relationship as P = k * v^3, where k is a constant of proportionality.

Given that a turbine generates 500 kW at a wind speed of 10 m/s, we can find k using the equation:

500 = k * 10^3

k = 500 / 1000

k = 0.5.

Now, to find out how much power the turbine would generate at 12 m/s. The calculation is :

P = 0.5 * 12^3

P = 0.5 * 1728

P = 864 kW.

The wind turbine generates 864 kW in a 12 m/s wind.

Answer:

65,1,5.5

Step-by-step explanation:

Replace with 1 and simplify.

Nicolas sells 5.125 pounds of shrimp per hour.

Therefore, he can sell 46.125 pounds of shrimp in 9 hours.

To determine how many pounds of shrimp Nicolas sold in one hour, we need to divide the total pounds of shrimp by the total number of hours.

Nicolas sold 20 1/2 pounds of shrimp in 4 hours.

Therefore, we divide 20.5 (which is the decimal equivalent of 20 1/2) by 4 to find the rate per hour:

20.5 ÷ 4 = 5.125

Nicolas sold 5.125 pounds of shrimp per hour.

To find out how many pounds he can sell in 9 hours, we multiply the rate per hour by 9:

5.125 × 9 = 46.125

Nicolas can sell 46.125 pounds of shrimp in 9 hours.

Answer: I think it 3/1

Step-by-step explanation: Because 2 to get to 5 is 3 and 5 to get to 6 is 3. Hope I am correct

Answer:

The ratio of girls to boys is 16:15

Step-by-step explanation:

To find this, we simply start by using the words.

Girls:Boys

Now we plug in the values.

16:15

The question requires us to use the exponential distribution to calculate the probability of waiting more than 15 minutes between two successive calls given a Poisson process with β parameter 1/6. We achieve this by using the cumulative distribution function. The probability is approximately 96.4%.

This question is essentially asking us to use the exponential distribution to calculate the probability of waiting for more than 15 minutes (which is 0.25 hour because we are dealing with hours as units of time) between two successive calls when the parameter β =1/6 is given. The exponential distribution is used to model the time between events in a Poisson process, and the probability density function is given by f(x) = βe^(-βx) for x ≥ 0.

The cumulative distribution function is F(x) = 1 - e^(-βx), so to compute the probability of waiting time that is more than 0.25 hour, we subtract the cumulative distribution function from 1.

So, P(X > 0.25) = 1 - P(X ≤ 0.25) = 1 - [1 - e^(-β * 0.25)] = e^(-β * 0.25) = e^(-(1/6) * 0.25) ≈ 0.964, or 96.4% as the answer.

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Answer:835.893

Step-by-step explanation:

do the interest rate thing you learned in class

if you didn't learn it im adding a picture on the bottom for help

Answer:

Prefix Symbol Multiplier

deci d 0.1

centi c 0.01

milli m 0.001

micro µ 0.000001

Step-by-step explanation:

Final answer:

78,045 rounded to the nearest thousand is 78,000. You round down because the hundreds digit (0) is less than 5. This approach to rounding applies in various arithmetic contexts.

Explanation:

To round 78,045 to the nearest thousand, we need to consider the hundreds digit, which is 0. In rounding, if the hundreds digit is 5 or greater, we would round up. However, because it is 0, we keep the thousands digit the same and replace all subsequent digits with zeros. Thus, 78,045 rounded to the nearest thousand is 78,000.

When dealing with whole numbers and rounding to a certain place value, it is crucial to look at the number to the immediate right of the place value you are rounding to. If this number is 5 or higher, you round up. Otherwise, you round down. This principle is true regardless of whether you are serving a subtraction operation, like 78,500 m - 362 m which rounds to 78,100 m, or if you're dealing with large numbers in scientific notation, such as 79,345 which can be represented as 7.9345 × 104.

Answer:

3/40

Step-by-step explanation:

After you multiply across, you get 3/40. Since these two numbers don't have common multiples, it just stays as 3/40

Answer:

the third option

Step-by-step explanation:

1*3= 3

10*4= 40

3/40

Answer:

(3, 7)

Step-by-step explanation:

The midpoint of a line joining the points  (x1, y1) and (x2, y2) has midpoint

[(x1 + x2)/ 2]. (y1 + y2)/2 ]

Substituting the given points:-

Midpoint of MN =  (-2 + 8)/2 ,  (4 + 10)/2

= 6/2 , 14/2

= (3, 7)   (answer)

Answer:

Let B represents the number of basil plants and F represents the number of fennel plants,

As per the given condition: Michelle has a maximum of 4500 milliliters  of water for her plants today. Each basil plant requires 350 of water, and each fennel plant requires 525  of water.

Each basil plant require 350 of water

⇒ total number of basil plant require water = 350B

Each Fennel plant require 525 of water.

⇒ total number of fennel plant require water = 525F

Since, Michelle has a maximum of 4500 milliliters of water;

then;

[tex]350B+525F \leq 4500[/tex]

Therefore, an inequality that represents the number of basil plants(B) and fennel plants can water today is; [tex]350B+525F \leq 4500[/tex]

Answers:

Mean = 13.55

Median = 13

Mode = 13

====================================================

Explanations

Mean:

To get the mean, multiply the ages with their corresponding frequencies. Then add up the results. I show this in the attached image below. The highlighted yellow cell is the sum of the x*y column (x = age, y = frequency). This value is 718.

Once you get to 718, you divide this over the total frequency which is 7+9+11+10+9+4+3 = 53 (so there is 53 people).

The mean is therefore 718/53 = 13.5471698113208 which rounds to 13.55

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

Median:

The median is the middle most value. There are 53 values here (add up the frequencies), so the midpoint is at slot 53/2 = 26.5 = 27. The first 26 values are below the median, and the last 26 values are above the median leaving 53-26-26 = 53 - 52 = 1 value in the very exact center.

Add up the frequencies starting from 7 then to 9, etc until you get to 27. So we have

7+9 = 16 which isn't 27

7+9+11 = 16+11 = 27 perfect, we landed on 27

This means that the last copy of 13 is in slot 27. This is because the last frequency added (11) corresponds to the age 13.

That is why the median is 13

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

Mode:

The mode is the most frequent value. Simply record the age that has the highest frequency. In this case, the highest frequency is 11 which corresponds to age 13, pointing to the mode being 13.