CAN SOMEONE HELP I WILL GIVE BRAINLIST IT'S DUE TODAY :(
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3


Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77


The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.

Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.

Three softball players discussed their batting averages after a game.


Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths


Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)

Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.

10%
30%
50%
90%

A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.


Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4


Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50


A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.

Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.

Determine the theoretical probability of the spinner not landing on blue, P(not blue).

0.375
0.625
0.750
0.875


A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3


Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77


A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.

A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.

Which statement about probability is true?

The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.

List the sample space for rolling a fair eight-sided die.

S = {1}
S = {8}
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8}

There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.


Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11




Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event

Which event will have a sample space of S = {h, t}?

Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B

ulia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?

Sample space = 1, 2, 3
Sample space = 1, 2, 3, 4, 5, 6
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape


Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.

Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

Answers

Answer 1

Answer:

Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.

0.23

If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.

Likely

Compare the probabilities and interpret the likelihood. Which statement is true?

Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)

Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.

90%

A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.

Outcome Frequency

Heart 7

Spade 3

Club 6

Diamond 4

Determine the experimental probability of drawing a spade.

0.15

A spinner with repeated colors numbered from 1 to 8 is shown.

Sections 1 and 8 are purple.

Sections 2 and 3 are yellow.

Sections 4, 5, and 6 are blue.

Section 7 is red.

Determine the theoretical probability of the spinner not landing on blue, P(not blue).

0.375

A spinner with repeated colors numbered from 1 to 8 is shown.

Sections 1 and 8 are purple.

Sections 2 and 3 are yellow.

Sections 4, 5, and 6 are blue.

Section 7 is orange.

Which statement about probability is true?

The probability of landing on orange is greater than the probability of landing on purple.

List the sample space for rolling a fair eight-sided die.

S = {1, 2, 3, 4, 5, 6, 7, 8}

There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.

Outcome Frequency

Brown 13

Black 9

Green 7

Gold 11

Likely

Equally likely and unlikely

Which event will have a sample space of S = {h, t}?

Flipping a fair, two-sided coin

Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?

Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape


Related Questions

A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts
down the slope, its speed is 4 m/s. 3 seconds later, at the bottom of the slope,
its speed is 22 m/s. What is the cars acceleration?

Answers

a=6m/s^2
Since acceleration=final speed-starting speed/time
acceleration=22-4/3=6m/s^2

A cylinder has a volume of 243 pi
and a diameter of 18. What is its height?

Answers

Answer:

0.955

Step-by-step explanation:

Height= volume x pi x radius squared (h = V x pi x r^2)

Volume (V) = 243

Height (h) = ?

Pi = 3.14

Radius (r) = 9

Diameter to radius = 18/2 = 9

h = 243 x 3.14 x 9^2

=0.955

The probability that a passenger is chosen for customs inspection is 10 %. Emma and Michael go through customs. What is the probability that neither of them is chosen for inspection? The probability of one passenger being chosen is independent of that of other passengers.
a) 81 %
b) 90 %
c) 99 %
d) other

Answers

The probability that neither of them is chosen for inspection is given as follows:

a) 81 %

What is the binomial distribution formula?

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

The parameter values for this problem are given as follows:

n = 2, p = 0.1.

The probability of neither is P(X = 0), hence:

P(X = 0) = (1 - 0.1)² = 0.81.

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What is the surface area of the polyhedron

Answers

Answer: equal to the sum of the area of all of its faces

Step-by-step explanation:

calculate the length of AC to 1 decvimL POINT

Answers

Answer:The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

What is the sum of the measures of the exterior angles of the polygon shown below? If necessary, round to the nearest tenth.
5 stars and like

Answers

The sum of the measures of the exterior angles of the polygon is,  360°

What is an angle ?

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

A polygon,

Having 9 equal sides,

The sum of the measures of the exterior angles of the polygon = ?

The sum of each interior & exterior angles are 180°

Suppose, interior angles  are respectively

a, b, c, d, e, f, g, h, i,

Now, exterior angles are respectively

180°-a, 180°-b, 180°-c, 180°-d, 180°-e, 180°-f, 180°-g, 180°-h, 180°-i,

The sum of the measures of the exterior angles of the polygon =

180°-a  + 180°-b +180°-c +180°-d + 180°-e + 180°-f  + 180°-g +180°-h + 180°-i,

1620 - (a + b + c + d + e + f + g + h + i)

Sum of all the interior angles  = (9-2)x180°

                                                  =  1260°

The sum of  the exterior angles of the polygon =  1620 - 1260°

                                                                               =   360°

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Write the phrase as an expression. a number x divided by 2

Answers

Answer: x/2

Step-by-step explanation: Good morning. I am not sure what you mean by "A number x", so I suppose that is a typo.

Answer: x/2 IS CORRECT

Step-by-step explanation:

I TRIED IT :)

What is the sum of 3 of the interior angles of a regular pentagon?
5 stars and like

Answers

Answer: 540°.

Step-by-step explanation:

by

Celine purchased a ball of red yarn costing $2.33. She gave the cashier $7.19. How much change did the cashier give back to Celine?

Answers

Answer:

$ 4.86

Step-by-step explanation:

Subtract 7.19 and 2.33

7.19-2.33=4.86

Assume the following

actual machine hours during the period of 54000 hours
estimates machine hours to be worked during the coming period of 55000 hours manufacturing overhead applied to production during the period of 432000 estimated variable manufacturing overhead per machine hour of 2.7

which is the fixed MOH cost

Answers

Based on the manufacturing overhead applied to production during the period of $432,000, the fixed manufacturing overhead cost is $286,200.

What is the manufacturing overhead applied?

The manufacturing overhead applied is determined as the product of the predetermined overhead rate and the actual machine hours consumed during the period.

Estimated machine hours to be worked = 55,000 hours

Actual machine hours during the period = 54,000 hours

Total manufacturing overhead applied to production = $432,000

Estimated variable manufacturing overhead per machine hour = $2.70

Total variable manufacturing overhead = $145,800 ($2.70 x 54,000)

Fixed manufacturing overhead (MOH) cost = $286,200 ($432,000 - $145,800)

Thus, the fixed manufacturing overhead cost is the difference ($286,200) between the total overhead cost applied and the variable manufacturing overhead cost.

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(x+2)^2=4(x+5)+y standard form

Answers

The standard form of the equation (x + 2)² = 4 (x + 5) + y is:

x² + y - 16 = 0

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The standard form of an equation is Ax + By = c.

Now,

(x + 2)² = 4 (x + 5) + y

x² + 4x + 4 = 4x + 20 + y

x² + 4 = 20 + y

x² + y = 20 - 4

x² + y = 16

x² + y - 16 = 0

Thus,

x² + y - 16 = 0 is the standard form of an equation.

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ria is buying plates and cubs for a party. she wants the same numbers of each.Plates are sold in packs of 8. cups are sold in packs of 12. what is the least number of plates and cups that ria can buy

Answers

The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

What is ratio?

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, ria is buying plates and cubs for a party. she wants the same numbers of each. Plates are sold in packs of 8. cups are sold in packs of 12.

Plates = 8 per pack

Cups = 12 per pack

the Lowest common multiple of 8 and 12

8 = 16, 24, 32, 40, 48, 56, 64, 72, 80

12 = 24, 36, 48, 60, 72

The Lowest common multiple of 8 and 12 is 24

The least number of plates and cups she can buy is 24

Packs of plates = 24 plates / 8 per pack

= 3 packs

She will buy 3 packs of plates

Packs of cups = 24 / 12 per pack

= 2 packs

She will buy 2 packs of cup

Therefore, The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

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evaluate without a calculator: sec 30°

Answers

Answer:

sec 30° = 1/cos 30° = 2.

Step-by-step explanation:

The secant function (sec) is the reciprocal of the cosine function. So, sec(x) = 1/cos(x). The value of cosine at 30 degrees is sqrt(3)/2, and its reciprocal is 2/sqrt(3), which can be simplified to 2. Hence, sec(30°) = 2.

URGENT!!!

Sharon invested $5,000 in a bond for 2 years. The total interest earned on the investment was $600. What was the interest rate on the investment?

Answers

The interest rate required to pay a simple interest of $600 from an investment of $5000 in 2 years is 6%.

What is the interest rate on the investment?

Simple interest is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $5,000Interest I = $600Elapsed time t = 2 yearsInterest rate r = ?

Plug the given values into the above formula and solve for r.

I = P × r × t

r = I / Pt

r = 600 / ( 5,000 × 2 )

r = 600 / ( 10,000 )

r = 0.06

Interest rate = r × 100%

Interest rate = 0.06 × 100%

Interest rate = 6%

Therefore, the interest rate is 6%.

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Describe how the graph of the function is a transformation of the original function f.

y=f(x+16)

Answers

The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.

For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.

In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.

2. What is the difference in rainfall from the wettest and driest months?

Answers

The difference in rainfall between the wettest and driest months is 3.97 inches.

What is a bar graph?

A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are utilized to contrast and compare various data types, frequencies, or other measurements of several categories of data.

On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.

Given the graph which shows the rainfall of the wettest and driest months,

here red blocks are for the driest months and blue blocks show the wettest months,

From the graph, we can see that the wettest month has a rainfall height of 2.3 inches

The driest month has a rainfall of -1.67 inches

So the difference between the two will be;

2.3 - (-1.67)

=  2.3 + 1.67 = 3.97 inches

Hence the difference is 3.97 inches.

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The complete question is,

The bar graph shows the differences in a city’s rainfall from the historical average. What is the difference in rainfall between the wettest and the driest months? Write your answer as a decimal.

The difference in rainfall between the wettest and the driest months is inches.

Which equation represents the graph? a graph of a line that passes through the points 0 comma negative 3 and 4 comma negative 1 y equals negative one half times x plus 6 y equals one half times x minus 3 y = 2x − 3 y = −2x + 6

Answers

the equation of  line passes through points (0, -3) and (4, -1) is 4y  = 3x -12.

What is a Linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, an equation of a line in the graph.

Since the graph shows that the line passes through points (0, -3) and (4, -1).

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept (value of y at x =0)

since

slope = (y - y')/(x -x')

In our case,

slope (m) = (-1 - (-3))/(4 -0)

m = 3/4

b = -3

Thus, the equation of the line:

y = 3/4x - 3

or, 4y  = 3x -12

therefore, the equation of the line will be 4y  = 3x -12.

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HELP
_______________

Answers

The correct statements regarding the translation from function f(x) to function g(x) are given as follows:

Function f is translated down 2 units.Function f is translated to left 3 units.

What is a translation?

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.

The translations for this problem are defined as follows:

x - 2 to x + 1 -> x = x + 3 -> translated left 3 units.y -> y - 2 -> translation down 2 units.

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in 2010 an earthquake below the ocean floor initiated a devastating tsunami in Samatra. scientists can approximate the velocity V in feet per second of a tsunami in water of depth d feet with the formula [tex]\sqrt{16} \\[/tex] [tex]\sqrt{d}[/tex]. Determine the velocity of a tsunami in 300 feet of water. Write your answer in simplified radical form.

Answers

Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

What is speed?

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation

v = √(16d)

a wave forms in water with a depth of 300 feet,

therefore d = 300 ft

so, we get,

velocity = √(16*300)

             = 4√300

             =4*17.32

             =69.28

Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

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A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people. Write a function relating the number of people, n, to the cost, C.

Answers

The value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people.

Hence, he value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

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I need this for math homework anyone on tonight to help? 5/8 = x/12 x=

Answers

x = 15/2

do u need an explanation?

How much is invested at 5% and 7%, with annual interest is $490, with a total of $8000

Answers

The amount invensted at 5% and 7% are 3500 and 4500 respectively.

What is a system of equations?

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,

For this we will establish the a system of equations,

x + y = 8000......(i)

0.05x + 0.07y = 490

Multiplying by 100,

5x + 7y = 49000.....(ii)

Multiplying eq(i) by 5,

5x + 5y = 40000

Subtract eq(i) from eq(ii)

2y = 9000

y = 4500

Put y = 4500 in eq(i)

x = 8000 - 4500

x = 3500

Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.

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Hey guys please help me with my quiz its about finding the values of letters in angles!!

Answers

The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

How to obtain the measures?

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

180 - (5x - 14) -> each angle is supplementary with it's external.44º.3x - 10.

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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13, 11, 9, 7 In the number pattern above, each term is 2 less than the previous term. Which of the following is also true about the pattern?
A. All the numbers are multiples of 3.
B. All the numbers are even.
C. All of the numbers are prime.
D. All the numbers are odd.

HURRY ITS DUE TODAY

Answers

The truth about the pattern that we have here is that all of the numbers are:    odd.

What are odd numbers?

In the number pattern given, each term is 2 less than the previous term. Starting from 13, we have 11 (13 - 2), 9 (11 - 2), and 7 (9 - 2). All of these numbers are odd, making answer D the correct choice.

A. All the numbers are multiples of 3: This is not true, as 9 is the only number that is a multiple of 3.

B. All the numbers are even: This is not true, as all of the numbers are odd.

C. All of the numbers are prime: This is not true, as 9 is not a prime number.

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I need help ASAP!!!!!

Answers

Answer:

Nope

Step-by-step explanation:

No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)

The sum of B and C is 90+45 which = 135

The sum of A and D is 90+135 which = 225

135 =/= 225

Find the surface area of the sphere. Use 3.14 for pi.

A. 1519.8 yd2

B. 276.3 yd2

C. 6079.0 yd2

D. 552.6 yd2

Answers

Answer:

A

Step-by-step explanation:

please memorize this formula for area of sphere

A=4π r²

so d = 22, which means r=11

so A = 4* π*11² = 4*121*π =484π = 1519.76

Please use the law of sines to show me how to solve the triangle please. Thank you .

Answers

Answer:

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\[/tex]

[tex]a=38.5[/tex] ft

[tex]b=51[/tex] ft

[tex]c=76[/tex] ft

Step-by-step explanation:

Here is the formula for the Law of Sines.

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]`

In this example we are given

[tex]\angle A =27.2 \textdegree\\\angle C=115.5 \textdegree\\c=76.0[/tex]

Angle B

The sum of the interior angles in a triangle add up to 180º. Given 2 angles, we can evaluate the 3rd.

[tex]180\textdegree-115.5\textdegree-27.2\textdegree=37.3 \textdegree[/tex]

[tex]\angle B=37.3 \textdegree[/tex]

Side a

We can use the Law of Sines formula  [tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]  to evaluate side a.

Inserting our values into the equation gives us

[tex]\frac{a}{\sin 27.2}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side a.

[tex]76*\sin 27.2=a*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 27.2}{\sin 115.5} =a[/tex]

[tex]38.49=a[/tex]

Side b

We can use the Law of Sines formula  [tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]  to evaluate side b.

Inserting our values into the equation gives us

[tex]\frac{b}{\sin 37.3}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side b.

[tex]76*\sin 37.3=b*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 37.3}{\sin 115.5} =b[/tex]

[tex]51.03=b[/tex]

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\a=38.5\\b=51\\c=76[/tex]

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sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

A solution contains furosemide (frusemide) 10 mg/mL. How many milligrams of frusemide are in 3 mL of solution?

Answers

Answer:

30mg

Step-by-step explanation:

10 mg/mL x 3 mL

solve the given initial-value problem. Dy dx + y = f(x), y(0) = 1, where f(x) = 1, 0 ≤ x ≤ 1; -1 , x ≥ 1

Answers

The general solution of the ODE is:

y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1

y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1

How did we get the values?

This is a first-order linear ordinary differential equation (ODE) with constant coefficients. It can be solved using the method of integrating factors.

Let's multiply both sides by the integrating factor e^(∫p(x)dx), where p(x) = 1.

e^(∫p(x)dx) * Dy/dx + e^(∫p(x)dx) * y = e^(∫p(x)dx) * f(x)

D/dx (e^(∫p(x)dx) * y) = e^(∫p(x)dx) * f(x)

Integrating both sides, we get:

e^(∫p(x)dx) * y = ∫ e^(∫p(x)dx) * f(x) dx + C

where C is an arbitrary constant of integration.

Using the initial condition y(0) = 1, we can find the value of the constant C.

y(0) = 1 = e^(∫p(x)dx) * y(0) = e^(∫p(x)dx) * 1 = ∫ e^(∫p(x)dx) * f(x) dx + C

So, C = 1 - ∫ e^(∫p(x)dx) * f(x) dx

For 0 ≤ x ≤ 1, we have f(x) = 1 and:

∫ e^(∫p(x)dx) * f(x) dx = ∫ e^x dx = (e^x - 1) / 1

For x ≥ 1, we have f(x) = -1 and:

∫ e^(∫p(x)dx) * f(x) dx = ∫ -e^x dx = -(e^x - 1) / 1

Therefore, the general solution of the ODE is:

y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1

y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1

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Write an expression to represent:
3
33 minus the product of
2
22 and

xx.

Answers

The expression to represent the given statement is:33 - (2 * 22 * ½x)

The expression "33 - (2 * 22 * ½x)" represents a mathematical calculation. Breaking it down, we start with the product of 2 multiplied by 22, which equals 44. Then, we multiply the result by ½x, where ½ represents one-half and x is a variable. This gives us the term 44 * ½x. Finally, we subtract this term from 33. In simpler terms, we have 33 minus half of 44 times x. The expression allows us to compute the value of the expression based on the input for the variable x, providing a way to evaluate the equation numerically.Let's dive deeper into the explanation.

The given expression is "33 - (2 * 22 * ½x)".

To simplify it, let's break it down step by step:

The term "2 * 22" is a multiplication operation that calculates the product of 2 and 22, resulting in 44.

Next, we have "½x". Here, ½ represents one-half, or 0.5. Multiplying 0.5 by x gives us 0.5x.

Putting it together, we have the term "44 * ½x". This means multiplying 44 by 0.5x, resulting in 22x.

Finally, we subtract the term "22x" from 33, giving us the expression "33 - 22x".

In summary, the expression represents the number 33 minus the product of 22 and the value of x, denoted as 22x. This expression allows us to calculate the result by substituting a specific value for x. It provides a way to compute the numerical outcome based on the given mathematical relationship.

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