Answer:
6√3 cm.
Step-by-step explanation:
The angle between the length of a rectangle and its diagonal is 30°. If the length of the rectangle is 6cm, find the length of the diagonal.
Let's call the width of the rectangle "w" and the diagonal "d". We know that the angle between the length and diagonal is 30 degrees, which means that the angle between the width and diagonal is 90 - 30 = 60 degrees (since the angles in a triangle add up to 180 degrees).
Now, we can use trigonometry to find the length of the diagonal. Specifically, we can use the sine function, which relates the lengths of the sides of a right triangle to the angles opposite them:
sin(angle) = opposite/hypotenuse
In this case, the angle we're interested in is 60 degrees, the opposite side is the width "w", and the hypotenuse is the diagonal "d". So we can write:
sin(60) = w/d
Solving for "d", we get:
d = w/sin(60)
Now we just need to find the width of the rectangle. Since we know the length of the rectangle is 6cm, we can use the fact that the opposite sides of a rectangle are equal to each other to write:
w = length*sin(30) = 6sin(30)
We can simplify sin(30) to 1/2, so:
w = 6/2 = 3
Now we can substitute this value of "w" into our expression for "d" to get:
d = w/sin(60) = 3/sin(60)
We can simplify sin(60) to √3/2, so:
d = 3/(√3/2) = 6/√3 = 2√3 * 2
So the length of the diagonal is 2√3 times the length of the width, or approximately 3.46 times the length of the width. Therefore, the length of the diagonal is:
d = 2√3 * 3 = 6√3 cm.
I need to know how to find the x,y, and z
Answer:
x =~ 31.2
y =~ 18
z =~ 9
Step-by-step explanation:
cos 30º = 27 / x
0.8660 = 27 / x
x = 27 / 0.8660
x =~ 31.18
w = height (smaller trinagle w, y, z)
tg 30º = w / 27
0.5774 = w / 27
w = 27 * 0.5774
w = 15.5898
tg 30º = z / 15.5898
0.5774 = z / 15.5898
z = 0.5774 * 15.5898
z = 9.00155052
cos 30º = 15.5898 / y
0.8660 = 15.5898 / y
y = 15.5898 / 0.8660
y =~ 18
Work out the volume of the cone radius is 3. 5 and length is 12
To work out the volume of the cone, we can use the formula V = (1/3) * π * r² * h, where r is the radius of the base of the cone and h is the height of the cone. The volume of the cone is approximately 171.55 cubic units.
The formula for calculating the volume of a cone is given as V = (1/3) * π * r² * h. In this formula, 'r' represents the radius of the base of the cone, and 'h' represents the height of the cone. By substituting the given values, the volume of the cone is calculated to be approximately 171.55 cubic units. This formula is widely used in various fields, such as architecture, engineering, and manufacturing. Calculating the volume of a cone is useful in determining the amount of material required to construct or fill a cone-shaped object, such as a cone-shaped container or a cone-shaped structure. The formula is also used in solving real-life problems related to cones, such as calculating the volume of ice cream in a cone-shaped ice cream cone or the volume of a cone-shaped tank used for storing liquids.
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(-2,-9), m= -7/5 write an equation in point slope form for the line that passes through each point with the given slope, then graph the equation.
The line passes through the two points (-2,-9) and (3,-16).
We can write an equation in point-slope form using the following formula for the line passing through the point (-2,-9) and having a slope of m = -7/5:
y - y1 = m(x - x1)
where m is the slope of the line and (x1,y1) is the line's point.
Inputting the values provided yields:
y - (-9) = (-7/5)(x - (-2))
Simplifying:
y + 9 = (-7/5)(x + 2)
To get rid of the fraction, multiply both sides by 5. This gives us:
5y + 45 = -7(x + 2)
As we enlarge and rearrange, we obtain:
7x + 5y + 59 = 0
This is the line's standard form equation.
We can locate two points on the line and plot them to create a graph of the line. We can utilise the y-intercept, which is obtained by solving for y while setting x=0 in the equation:
7(0) + 5y + 59 = 0
5y = -59
y = -59/5
The y-intercept is therefore (0,-59/5). Using the slope, we may also locate a different point on the line:
m = -7/5
Beginning at (-2,-9), we can travel 7 units left and 5 units right to reach a different point:
(-2+5, -9-7) = (3, -16) (3, -16)
Hence, the line traverses both of the following two points: (3,-16).
Here is the line's graph:
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\ |
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-------*-----------------
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3|
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2|
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1|
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The answer is:
[tex]\sf{y+9=-\dfrac{7}{5}(x+2)}[/tex]
Work/explanation:
We need to determine the line's equation. I will begin by writing the equation in point slope form:
[tex]\mapsto\phantom{333}\sf{y-y_1=m(x-x_1)}[/tex]
where m = slope and (x₁,y₁) is the point
Plug in the data:
[tex]\sf{y-(-9)=-\dfrac{7}{5}(x-(-2)}[/tex]
Simplify
[tex]\sf{y+9=-\dfrac{7}{5}(x+2)}[/tex]
Hence, this is the equation.2. A boat traveling at 30 miles per hour with a tow line of 400 feet will give a parasail rider a height of 300 feet.
a) Draw and label a diagram to represent this situation. (2 points)
b) What is the angle of elevation from the boat to the parasail rider? (5 points)
c) What is the horizontal distance from the parasail rider to the boat? (5 points)
d) What do you notice about the angle of elevation of this flight compared to the. anale of elevation of the flight described in Exercise 1? Use trigonometric functions to explain wny this is true. (10 points)
e) What conclusion can you draw about angles of elevation for parasailing boats traveling at the same speed? (10 points)2. A boat traveling at 30 miles per hour with a tow line of 400 feet will give a parasail rider a height of 300 feet.
a) Draw and label a diagram to represent this situation. (2 points)
b) What is the angle of elevation from the boat to the parasail rider? (5 points)
c) What is the horizontal distance from the parasail rider to the boat? (5 points)
d) What do you notice about the angle of elevation of this flight compared to the. anale of elevation of the flight described in Exercise 1? Use trigonometric functions to explain wny this is true. (10 points)
e) What conclusion can you draw about angles of elevation for parasailing boats traveling at the same speed? (10 points)
The angle of elevation is approximately 36.87 degrees and the horizontal distance is 264.6 feet
What is the angle of elevation from the boat to the parasail ridera.
The diagram is attached below;
b. We can use the tangent function to find the angle of elevation:
tan(θ) = opposite / adjacent
tan(θ) = 300 / 400
tan(θ) = 0.75
θ = tan^(-1)(0.75)
θ ≈ 36.87 degrees
So the angle of elevation from the boat to the parasail rider is approximately 36.87 degrees.
c. We can use the Pythagorean theorem to find the horizontal distance from the parasail rider to the boat:
d = √(400^2 - 300^2)
d ≈ 264.6 feet
So the horizontal distance from the parasail rider to the boat is approximately 265 feet.
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Painters painted half of a wall yellow, their boss told them it was supposed to be painted red, they waited for it to dry and then started covering the yellow with red. At the end of the day, 5/6 of the yellow was painted red, how much of the whole wall had been painted red.
Answer: 1/6
Step-by-step explanation:
1/1 - 5/6
2 6-5/6
2 1/6
Is this relationship a direct variation X -3 2 1 y -4 6 4
the relationship between x and y given by the values (-3, -4), (2, 6), and (1, 4) is not a direct variation.
To determine whether the relationship between x and y is a direct variation, we need to check if y is directly proportional to x. In other words, we need to check if there is a constant of proportionality that relates the two variables.
To do this, we can calculate the ratio of y to x for each pair of corresponding values:
y/x = (-4)/(-3) = 4/2 = 2
y/x = 6/2 = 3
y/x = 4/1 = 4
If y is directly proportional to x, then the ratio of y to x should be the same for all pairs of corresponding values. However, in this case, the ratios are not equal. Therefore, the relationship between x and y is not a direct variation.
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face A
2cm
20%
face B
2cm
Both watch faces are circular with radius 2cm.
The materials used to make both watch faces have the same thickness.
A is made entirely of plastic.
B has a 20° sector of metal and à 340° sector of plastic.
The ratio of the cost per cm² of the metal to the cost per cm² of the plastic is 3:2
Work out the ratio of the cost of the materials for A to the cost of the materials for B.
Give your answer in its simplest form.
You must show all your working.
Therefore , the solution of the given problem of ratio comes out to be 8:17 .
Describe ratio.The simple formula "a / b," where "b" may be greater than zero, can be used to determine a group of integers "a" and "b" that appear to be equal. Two ratios are combined to form a ratio. If there were only one man and three ladies, the fraction would be 1:1. In the group, there are 3/4 women and 1/4 males. Parts can be a division between things, a figure, or a particular percentage of a component's volume.
Here,
Let x be the price of plastic per square centimetre used to create visage A.
Consequently, the price of the components for aspect A is:
=> 4πx
The metal sector's size on face B is:
=> (20/360)π(2cm)² = (1/9)π cm²
The plastic sector's size on face B is:
=> (340/360)π(2cm)² = (17/9)π cm²
Face B's entire surface size is:
=> (1/9)π + (17/9)π = 2π cm²
Let y be the plastic's expense per square centimetre used to create face B.
Consequently, the price per cm2 of the metal used to create face B is three and a half times the price per cm2 of the plastic, leading to:
=> (3/2)y = (3/2)(2x) = 3x
The material cost for the metal section on face B is inversely correlated with its area, so:
=> (1/9)π(3x)
The price of the plastic used in the section on face B is inversely proportional to its area, so:
=> (17/9)πy
=> 8πx : 17πy = 8 : 17
The response is 8:17,
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in a class of 40 students,18 passed maths,19passed account,16 passed economics,5 passed math and accounts only,6maths only,9accounts only,2account and economics only,if each students offered at least one of the subjects:how many failed in all the subjects. (b) find the percentage number who failed in at least one of economics and mathematics. (c). calculate the probability that a student at random failed?
a. The number of students that failed in all subject is 4
b. The percentage of students who failed one of economic and mathematics is 5.2%
c. The probability that a student at random failed is 1/10
What is set?A set is defined as the collect of item with similarities.
n( of student that passed math only) = 6
n( of students that passed account only) = 9
n( of students that passed economics only) = 16-(4+3+2)
= 16-9 = 7
n ( of student that passed math and account only) = 5
n( of student that passed account and economics only) = 2
n ( of student that passed math and economics only) = 18-(5+3+y) = 6
= 18-8-y = 6
= 10-y = 6
y = 4
n( of students that passed all the three subjects) =19-( 5+2+x) = 9
= 19-7-x = 9
= 12 -x = 9
-x = -3
x = 3
a. Therefore no of student that failed all subject =
6+9+7+5+2+4+3+z = 40
36+z = 40
z = 40-36 = 4
b. Student that failed at least math and economics = 4+9 = 13
= 13/40 × 100 = 5.2%
c. probability that a student at random failed = 4/40 = 1/10
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Line A (y= 2x+4) is transformed into Line B(y=x-9) Which best describes the new slope and y-intercept?
The slope is __ and the line is shifted ___
complete the blanks
The line is 13 units to the right (or shifted by -13 units).
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign.
When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
According to our question-
The ratio of y to x, which indicates how many units change in y when a specific number of units change in x, is used to express a line's slope.
A has a slope of 2 (x factor) = 2/1.
and as a result, y moves 2 units while x moves 1 unit.
B has a slope of 1 = 1/1.
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Given:
AC‾ \overline{AC}
AC
and
BD‾\overline{BD}
BD
bisect each other.
Prove:
△BEC≅△DEA\triangle BEC \cong \triangle DEA
△BEC≅△DEA.
As a result of angle-angle-side (AAS) alignment, we have ABO, DBO, and AEO, CEO.
To prove △BEC≅△DEA:
First, we can see that segment AC and segment BD intersect at point O, which is the point of intersection of the angle bisectors of △BED.
Since AC and BD are angle bisectors, they are perpendicular bisectors of each other, so they divide the angles of △BED into congruent angles.
This means that angle ABO is congruent to angle DBO, and angle AEO is congruent to angle CEO.
Since angle ABO and angle AEO are vertical angles, they are congruent.
Similarly, angle DBO and angle CEO are vertical angles, so they are congruent.
Therefore, we have △ABO≅△DBO and △AEO≅△CEO by angle-angle-side (AAS) congruence.
Since BE is common to both triangles, we can conclude that △BEC≅△DEA by side-angle-side (SAS) congruence.
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Helen is about to ride a straight water slide. The launching platform is at the top of a tower that is 21 feet tall. The splash pool at the end of the slide is 72 feet from the base of the tower. How long is the water slide itself?
feet=
The length of the slide itself in feet would be = 75 ft.
How to calculate the length of the water slide?To calculate the length of the water slide the Pythagorean formula should be used which is written as follows;
C² = a² + b²
a = length of the tower = 21 ft
b = distance from the base of the tower = 72ft
C = length of the water slide = ?
c² = 21²+72²
C² = 441 + 5184
c² = 5625
C = √5625
C = 75 ft
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try
(x
-2y = 16)
(- 6x +5y =-26)
x
-2y = 16
-6x +5y = -26
=
0 |xo|y=
Answer: I belive the answer is 0lxoly+39.56
Step-by-step explanation:
SIKE
4x+3y=21 and 4x+2y=16
Solve the simentaneous equations
the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.
We can solve this system of equations using either substitution or elimination method.
Using substitution method:
From the second equation, we can solve for x in terms of y:
4x + 2y = 16
4x = 16 - 2y
x = 4 - (1/2)y
Substitute this expression for x into the first equation:
4x + 3y = 21
4(4 - (1/2)y) + 3y = 21
16 - 2y + 3y = 21
y = 5
Now, substitute y = 5 into either of the original equations to solve for x:
4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 6
x = 3/2
Therefore, the solution to is x = 3/2 and y = 5.
We can check this solution by substituting x = 3/2 and y = 5 into both equations:
4x + 3y = 21
4(3/2) + 3(5) = 6 + 15 = 21
and 4x + 2y = 16
4(3/2) + 2(5) = 6 + 10 = 16
So the solution (x = 3/2, y = 5) satisfies both equations, and therefore it is the correct solution.
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(7.2 x 1017) x (7.5 x 10-9 X (3.6 x 10-8) x (2.5 x 1010) X
Answer:
Step-by-step explanation:
483278.4
Premise: All multiples of 9 are multiples of 3. Premise: 57 is a multiple of 3. Conclusion: 57 is a multiple of 9.
Answer:
The conclusion is false.
Step-by-step explanation:
[tex]\frac{57}{3} = 19\\\\\frac{9}{3} = 3[/tex]
Although 3 and 9 do share some multiples, they must be divisible by 3. For example. 36/3 = 12, and 12 is divisible by 3. However, 57/3 = 19, which is not divisible by 3.
Error Analysis Adding and subtracting fractions
In addition of fractions together student added the denominators together, which is the error in solution. You must have like denominators in order to add fractions together is the strategy for solution. Haley bought 7/8 pound of cheese.
We have a incorrect solution of problem consists addition and subtraction fractions. We have to identify error and solve problem correctly and also share a strategy for solution. Now the problem is defined as : Quantity of mozzarella cheese bought by Haley = [tex] \frac{3}{8} [/tex] pound
Quantity of parmesan cheese bought by Haley = [tex] \frac{1}{2} [/tex] pound
Total pound of cheese that she did bought = sum of parmesan cheese and mozzarella cheese
= [tex] \frac{3}{8} + \frac{1}{2} [/tex]
Incorrect work:
[tex] \frac{3}{8} + \frac{1}{2} = \frac{4}{10}[/tex] [tex]= \frac{2}{5} [/tex]
Identification and Explain the Error :
In the problem student correctly identified that this was addition of fractions however he was incorrect in solving. When adding fractions together you do not add denominators together.
He also forgot that you must have "like" denominators.
Correct Solution:
[tex] \frac{3}{8} + \frac{1}{2} [/tex]
For addition of fractions, make the same denominator in both of fractions. So, multiply the denominator and numentor in fraction 1/2 by 4.
[tex] = \frac{3}{8} + \frac{1 \times 4}{2\times 4} = \frac{3}{8} + \frac{4}{8} [/tex][tex] =\frac{7}{8} [/tex], which is the required solution.
Strategy: We do not add denominator together ever. You must have like denominators in order to add them together. Hence, Haley bought 7/8 pound of cheese.
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Complete question:
Error Analysis Adding and subtracting fractions :
Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then share a strategy this student could use to prevent the same error in the future. Haley bought 3/8 pound of mozzarella cheese and 1/2 pound of parmesan cheese. How many pound of cheese did she buy?
Incorrect work or solution : 3/8 + 1/2
= 4/10 = 2/5
Haley bought 2/5 pound of cheese.
PLEASE HELP!! I NEED HELP
Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The parameters for the trip are given as follows:
Distance of 230 miles.Time of 7 hours.Hence the velocity is obtained as follows:
230/7 = 32.86 miles per hour.
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Simplify this expression
Show you work using the CER strategy.
4(8x + 1)-6(1-8x)
4)
A basket contains four types of fruits. Cherries, Bananas, Green apples and water melons.
What is the proportion of
a) Cherries? b) green apples?
b) Ratio of water melons to bananas?
The proportion of green apples can be estimated in the same way: expressions Green apple proportion = (number of green apples) / (Total number of fruits)
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that contains variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical sign +.
a) Because the basket contains four different types of fruits, the proportion of cherries can be computed as follows:
Cherry proportion = (number of cherries) / (Total number of fruits)
We can't compute the proportion of cherries without knowing how many fruits are in the basket.
b) The proportion of green apples can be estimated in the same way:
Green apple proportion = (number of green apples) / (Total number of fruits)
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Sarah invested £12 000 in a unit trust five years ago.
The value of the unit trust has increased by 7% per annum for each of the last 3 years.
Before this, the price had decreased by 3% per annum.
Calculate the current price of the unit trust.
Give your answer to the nearest whole number of pounds.
Answer:efefef
Step-by-step explanation:
efregtythth
On a scale drawing of a dock for a marina, 1 inch equals 18 feet. The dock is 250 feet long. What is the length of the dock on the scale drawing?
The length of the dock on the scale drawing would be 13.89 inches (250/18 = 13.89).
On a scale drawing of a dock for a marina, 1 inch equals 18 feet. This means that for every inch on the scale drawing, it represents 18 feet in reality. The dock is 250 feet long. To calculate the length of the dock on the scale drawing, divide 250 by 18. This gives the result of 13.89. This means that the length of the dock on the scale drawing is 13.89 inches. This is because for every inch on the scale drawing, it represents 18 feet in reality. Therefore, the length of the dock on the scale drawing is 13.89 inches (250/18 = 13.89). To ensure accuracy, the calculation should be double checked. This can be done by multiplying 13.89 by 18 which should give the result of 250. This confirms that the length of the dock on the scale drawing is 13.89 inches.
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Write a standard form quadratic equation with -2 and 3 as solutions
x² - x - 6 = 0 is the standard form quadratic equation with solutions of -2 and 3.
A quadratic equation with two solutions is what?There are two roots—or solutions—to a quadratic equation with real or complex coefficients. These two possibilities may or may not be distinct, and they may or may not be true. The standard quadratic equation, Y=x2x6, can be solved using the set of solutions 2, 3, which are given.
The elements of a quadratic equation whose solutions are -2 and 3 are (x + 2) and (3, respectively) (x - 3).
The total value of the quadratic equation is 0.
We can add the two elements together to obtain the quadratic equation in standard form:
(x + 2) (x - 3) = x²-3x+2x-6
Simplifying this expression, we get:
x²- x - 6 = 0
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Please helppp!!!!!!!!!!!!
The length of the arc of the sector is approximately 34.6 millimeters when rounded to one decimal place.
What is angle ?
An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are often referred to as the sides of the angle. Angles are typically measured in degrees or radians and are used to describe the amount of turn between two lines or surfaces.
In a circle, the measure of the arc of a sector is proportional to the measure of the central angle that it subtends. Therefore, to find the length of the arc of the sector in this problem, we need to first find the measure of the central angle that corresponds to the inscribed angle of 312 degrees.
The measure of the central angle is equal to twice the measure of the inscribed angle, which is 312/2 = 156 degrees. This is because the inscribed angle subtends an arc that is half as long as the arc subtended by the central angle.
The length of the arc of the sector can be calculated using the formula:
arc length = (central angle / 360 degrees) x (2 x pi x radius)
Plugging in the values we have:
arc length = (156/360) x (2 x pi x 4mm)
arc length = (13/30) x (8pi)
arc length = (104/30) x pi
arc length ≈ 34.557mm
Therefore, the length of the arc of the sector is approximately 34.6 millimeters when rounded to one decimal place.
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Suppose a normal distribution has a mean of 62 and a standard deviation of
4. What is the probability that a data value is between 55 and 63? Round your
answer to the nearest tenth of a percent.
O A. 55.9%
O B. 56.9%
O C. 53.9%
O D. 54.9%
Answer:To solve this problem, we need to standardize the values of 55 and 63 to z-scores and then use the standard normal distribution table to find the area between those two z-scores.
The z-score for a value of 55 is:
z = (55 - 62) / 4 = -1.75
The z-score for a value of 63 is:
z = (63 - 62) / 4 = 0.25
Using a standard normal distribution table, we can find that the area to the left of z = -1.75 is 0.0401 and the area to the left of z = 0.25 is 0.5987. Therefore, the area between z = -1.75 and z = 0.25 is:
0.5987 - 0.0401 = 0.5586
To convert this area back to a percentage, we multiply by 100:
0.5586 * 100 ≈ 55.9%
Therefore, the answer is A. 55.9%.
Step-by-step explanation:
lighthouse sits at the edge of a cliff, as shown. A ship at sea level is 825 meters from the base of the cliff. The angle of elevation from sea level to the base of
he lighthouse is 37.2". The angle of elevation from sea level to the top of the lighthouse is 38.3°. Find the height of the lighthouse from the top of the cliff.
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.
The height of the lighthouse from the top of the cliff is given as 25.3 cm
How to solve for the heighttan 37.2 = h / 825
h = 825 * 0.7590
h = 626.209
tan 38.3 = 626.209 + a / 825
825 tan 38.3 = 626.209 + a
651.55 = 626.209 + a
a = 651.55 - 626.209
a = 25 . 33 meters
Hence we can say that the height of the lighthouse from the top of the cliff is given as 25 . 33 meters
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Which algebraic expression is equivalent to the expression below? 6(9 + 5x) + 14 A. 30x - 68 B. 30x + 68 C. 30x + 40 D. 5x + 68
Answer:
[tex]30x +68[/tex]
Step-by-step explanation:
[tex]6(9+5x)+14[/tex]
[tex]\text{Distribute the 6}[/tex]
[tex]30x +68[/tex]
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1).
Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.)
questions to answer:
What is Miguel’s expected value from playing the game?
Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays?
What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.
On average, Miguel loses half a dollar every time he plays.
How to solve
To check all the events (6), we label the chips.
Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices.
Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one.
The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$.
In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on.
On average, Miguel loses half a dollar every time he plays.
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The lateral area of the smaller cylinder is 25pi and the lateral area of the larger cylinder is 64pi. If the volume of the smaller cylinder is 150pi, what is the volume of the larger cylinder?
The volume of the larger cylinder is (25/8)πR³.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in units of cubic meters, cubic centimeters, cubic feet.
According to question:Let's denote the radius and height of the smaller cylinder as r and h, respectively, and the radius and height of the larger cylinder as R and H, respectively.
We know that the lateral area of a cylinder is given by the formula:
Lateral area = 2πrh
Using this formula for the smaller and larger cylinders, we get:
25π = 2πrh
64π = 2πRH
Dividing both sides of the first equation by 2π, we get:
rh = 25/2π
We also know that the following formula determines a cylinder's volume:
Volume = πr²h
Using this formula for the smaller cylinder, we get:
150π = πr²h
Substituting rh = 25/2π from above, we get:
150π = πr²(25/2π)
r² = 12
Taking the square root of both sides, we get:
r = √12 = 2√3
Substituting this value into rh = 25/2π, we get:
h = 25/(2πr) = 25/(4π√3)
Now, we can use the ratio of the lateral areas to find the ratio of the heights:
25π/64π = (2πrh)/(2πRH)
25/64 = rh/RH
25/64 = (2√3)(25)/(4πR)(H)
H = 2hR/r
Finally, we can use the formula for the volume of the larger cylinder to find its volume:
Volume = πR²H
Volume = πR²(2hR/r)
Volume = 2πR³h/r
Substituting the values we found for r, h, and H, we get:
Volume = 2π(R³)(25/(4π√3))/(2√3)
Volume = (25/8)πR³
Therefore, the volume of the larger cylinder is (25/8)πR³.
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In a school of 145 students, each was asked to choose one or more activities from sport, music and drama. 76 students choosr sport, 64 chose music and 40 students chose drama. 12 students chose both music and sport, 7 chose both sport and drama, and 21 chose both music and drama. How many students chose all three activities?
7 number of students chose all three activities.
To find out how many students chose all three activities, we need to subtract the number of students who chose two activities from the total number of students. There are 76 students who chose sport, 64 students who chose music, and 40 students who chose drama. 12 students chose both music and sport, 7 chose both sport and drama, and 21 chose both music and drama. We can subtract these two-activity choosers from the total number of students to find out how many chose all three activities: 145 - (12 + 7 + 21) = 105. Therefore, 7 students chose all three activities.
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if anyone could help, would be much appreciated
[tex]g( \sqrt{55} ) = ( \sqrt{55} ) {}^{2} + 11 = 55 + 11 = 66[/tex]
[tex]f(g(55)) = f(66) = \sqrt{66 - 2} = \sqrt{64} = 8[/tex]
The value of the function f(g(√55)) is 3√7.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
We have the function:
f(x) = √ (x - 2)
and, g(x) = x² + 11.
As, g(√55)
= (√55)² + 11
= 55 + 11
= 66
So, f(g(√55))
= √ (65 - 2)
= √63
= 3√7
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