Answer:
10 outcomes
Step-by-step explanation:
if 2 coins were selected with replacement=10×10=100
number of outcomes if 2 coins were selected without replacement=10×9=90
Finally, 100-90= 10 outcomes!
If BA = 5x + 5 and AD = 10x - 20, find BD. It is a parallelogram by the way.
To find the length of BD in a parallelogram where BA = 5x + 5 and AD = 10x - 20, we use the fact that opposite sides of a parallelogram are equal in length. Therefore, BD = BA = 30.
Since it is a parallelogram, we know that opposite sides are equal. So, BD = BA = 5x + 5. To find the value of x, we can use the fact that AD is also equal to BD. So, we can set the two expressions for BD equal to each other
5x + 5 = 10x - 20
Simplifying and solving for x, we get
5x = 25
x = 5
Now we can substitute x back into the expression for BD to get the final answer
BD = 5x + 5 = 5(5) + 5 = 30
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What are the slopes and y-intercept of a graph?
The slopes and y-intercept of a graph are two key components of the equation that describes the relationship between two variables.
The slope of a graph is the measure of how steeply the line is rising or falling. It is calculated by dividing the change in the y-axis by the change in the x-axis between two points on the line. A positive slope indicates that the line is rising, while a negative slope indicates that the line is falling.
The y-intercept of a graph is the point where the line crosses the y-axis. It is the value of y when x=0. The y-intercept is a fixed point on the line and is used to help determine the equation of the line.
Together, the slope and y-intercept of a graph can be used to write an equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
Help with problem in photo pls
Check the picture below.
a laundromat has 5 washing machines. a typical machine breaks down once every 5 days. a repairer can repair a machine in an average of 2.5 days. currently, three repairers are on duty. the owner of the laundromat has the option of replacing them with a superworker, who can repair a machine in an average of 5 6 day. the salary of the superworker equals the pay of the three regular employees. breakdown and service times are exponential. should the laundromat replace the three repairers with the superworker?
Replacing three repairers with a superworker would be cost-effective for the laundromat as the expected repair time would increase and lead to more downtime for the machines.
To determine if the laundromat should replace the three repairers with the superworker, we need to compare the expected repair time under each scenario.
With three repairers, the expected time to repair a machine is the sum of the expected time until a machine breaks down and the expected time for a repairer to fix it
E(time with three repairers) = 5 + 2.5/3 = 6.167 days.
With the superworker, the expected time to repair a machine is
E(time with superworker) = 5/6 = 0.833 days.
Therefore, on average, it takes much less time to repair a machine with the superworker than with three repairers. Since the salary of the superworker is equal to that of three repairers, the laundromat should replace the three repairers with the superworker. It is also more cost-effective.
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Find the volume of this cylinder using 3.14 as pi
13 ft
20 ft
The value of the volume of the cylinder is 706. 5 cm³
How to determine the valueThe formula for the volume of a cylinder is expressed as;
V = πr²h
Such that the parameters are;
V is the volume of the cylinderπ takes the value 3.14r is the radius of the cylinderh is the height of the cylinderNow, substitute the values into the formula, we get;
Volume, V = 3.14 × 5² × 9
Find the square value and substitute
Volume, V = 3.14 × 25 × 9
Multiply the values
volume, V = 706. 5 cm³
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What is the value of the h in the triangle below?
The value of h in the triangle shown above is calculated using proportion as: h = 4.
How to Find the Value of h in the Triangle?The two triangles shown are similar to each other based on the Angle-angle (AA) Similarity theorem. This implies that the length of their corresponding pair of sides would be proportional to each other.
Therefore, we have:
8/18 = h/9 [proportional sides of similar triangles]
Cross multiply:
h * 18 = 8 * 9
18h = 72
Divide both sides by 18:
18h/18 = 72/18 [Division property of equality]
h = 4
Therefore, the length of h in the given image is determined as: 4 units.
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Solve the system of equation and explain geometrically how you know that your answers are solutions to the system. x^2+y^2 =100 and 3x - y = 30 how you know
The solution of the system of equations is given by the ordered pairs [10, 0] and [8, -6].
How to graphically solve this system of equations?In order to graphically solve the given system of equations on a coordinate plane, we would use an online graphing calculator to create a plot of the system of equations and then determine their point of intersection;
x² + y² = 100 ......equation 1.
3x - y = 30 ......equation 2.
Based on the graph shown in the image attached above, we can reasonably infer and logically deduce that the solution to this system of equations lies in both Quadrant I and Quadrant IV, and it is represented by this ordered pairs (10, 0) and (8, -6).
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Let L be the line of intersection between the planes x + y - 2z = 1, 4x + y + 3z = 4.
(a) Find a vector v parallel to L. V= (b) Find the cartesian equation of a plane through the point (2, -1, 3) and perpendicular to L.
(a) A vector v parallel to the line of intersection L is v = <1, 1, -2>. (b) The cartesian equation of the plane is -7x + 10y - 3z = -1
(a) To find a vector v parallel to the line of intersection L, we need to take the cross product of the normal vectors to the two given planes. The normal vectors are the coefficients of x, y, and z in the equations of the planes.
In this case, the equations of the planes are:
x + y - 2z = 1
4x + y + 3z = 4
The normal vectors to these planes are <1, 1, -2> and <4, 1, 3>, respectively. Since the line of intersection is parallel to both planes, a vector parallel to the line must be perpendicular to both normal vectors.
We can find such a vector by taking the cross product of the two normal vectors, which gives us: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
Therefore, a vector v = <1, 1, -2>.
(b) To find the equation of the plane through the point (2, -1, 3) and perpendicular to L, we need to find a normal vector to the plane that is also parallel to L.
We can find such a vector by taking the cross product of the normal vectors to the two given planes. The normal vectors are <1, 1, -2> and <4, 1, 3>, so the cross product is: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>
This vector is parallel to L, so it can serve as the normal vector to the desired plane. The equation of the plane can be written in point-normal form as: -7(x - 2) + 10(y + 1) - 3(z - 3) = 0
Simplifying, we get:
-7x + 10y - 3z = -1
Therefore, the cartesian equation of the plane is -7x + 10y - 3z = -1, and it passes through the point (2, -1, 3) and is perpendicular to the line of intersection between the given planes.
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A buoy is floating in the water near a lighthouse. The height of the lighthouse is 18 meters, and the horizontal distance from the buoy to the base of the lighthouse is 45 meters. What is the approximate angle of elevation from the buoy to the top of the lighthouse, rounded to the nearest whole degree?
The equivalent expression is $\boxed{4^{15} \cdot 5^{10}}$.
Find out the simplified expression inside the parentheses?We can simplify the expression inside the parentheses first, using the rule that says when you raise a power to another power, you multiply the exponents:
$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$
Now, we can use the rule that says when you raise a product to a power, you raise each factor to the power:
$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$
Simplifying further:
$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$
we can substitute this expression back into the original expression:
$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$
To simplify this expression further, we can use the rule that says when you raise a product to a power, you raise each factor to the power:
$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$
Simplifying the exponents, we get:
$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$
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2 x (2a x 7) PLEASE HELP ME PLEASE I WILL DO ANYTHING
If f(x) = x2 + 4x + 6, find the following values. = 1. f(a) = 2. f(a - 1) = 3. f(a + 1) =
To find the values of f(a), f(a-1), and f(a+1) when f(x) = x^2 + 4x + 6, So, the values are: f(a) = a^2 + 4a + 6, f(a-1) = a^2 + 6a + 3, f(a+1) = a^2 + 6a + 11.
we simply substitute the given values of a into the function.
1. f(a) = a^2 + 4a + 6
2. f(a-1) = (a-1)^2 + 4(a-1) + 6 = a^2 + 2a + 1 + 4a - 4 + 6 = a^2 + 6a + 3
3. f(a+1) = (a+1)^2 + 4(a+1) + 6 = a^2 + 2a + 1 + 4a + 4 + 6 = a^2 + 6a + 11
So, the values are:
1. f(a) = a^2 + 4a + 6
2. f(a-1) = a^2 + 6a + 3
3. f(a+1) = a^2 + 6a + 11
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The product of 58 and the quantity 8b plus 8.
Expression[tex]58(8b+8)[/tex]simplifies to[tex]464b+464.[/tex]
How to simplify quantity expressions?
Calculate the product of 58 and the quantity 8b + 8
The given expression is:
[tex]58(8b + 8)[/tex]
Multiplying 58 by 8b and 8, we get:
[tex]464b + 464[/tex]
Therefore, the answer is:
[tex]58(8b + 8) = 464b + 464[/tex]
To find the product of 58 and the quantity 8b + 8, we need to use the distributive property of multiplication over addition, which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can distribute 58 over 8b and 8, as follows:
[tex]58(8b + 8) = 58 × 8b + 58 × 8[/tex]
Multiplying 58 by 8b and 8 separately, we get:
[tex]58 × 8b = 464b[/tex]
[tex]58 × 8 = 464[/tex]
Adding the products, we get the final answer:
[tex]58(8b + 8) = 464b + 464[/tex]
Therefore, the expression [tex]58(8b + 8)[/tex]simplifies to[tex]464b + 464.[/tex]
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A radar antenna is located on a ship that is 4 kilometres from a straight shore. It is rotating at 32 revolutions per minute. How fast does the radar beam sweep along the shore when the angle between the beam and the shortest distance to the shore is Pi/4 radians?
The radar beam moves at a pace of roughly 536.47 kilometers per hour as it scans the coastline.
Let A represent the location of the radar antenna and B represent the shoreline location that is closest to A. Let C represent the radar beam's current location on the coast and Ф represent the angle between the beam and the line AB. As a result, we obtain a right triangle ABC, where AB is equal to 4 km, and BC is the length at which the radar beam sweeps along the shore.
32 rev/min(2π/60 sec) = 3.36 radians/sec. BC = r(Ф) = (4 km)(π/4) = π km.
We may calculate the radar beam's speed down the shore by multiplying these two values:
(536.47 km/hr) = 10.54 km/sec or (3.36 rad/sec)(π km).
Hence, the of sweeping is 10.54 km/sec.
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Please help me now Asapppp
So the angles that must be right angles are KER and ERI.
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 usually denoted by the letters A and B, and the vertex is denoted by the letter V. The angle is denoted by the symbol ∠, followed by the letters of the rays with the vertex in between, such as ∠AVB. The measure of an angle is the amount of rotation needed to move one ray to coincide with the other ray, and is usually given in degrees or radians. Angles are used in many areas of mathematics and science, such as trigonometry, geometry, physics, and engineering. They are also used in everyday life, such as in navigation, construction, and design.
Here,
Since RE and RI are secants of the circle, we can use the Intersecting Secants Theorem to find the relationships between the angles in the diagram.
Angle ERK is half of the intercepted arc EIK, so we have m∠ERK = 1/2m(arc EIK).
Similarly, angle KRI is half of the intercepted arc KE, so we have m∠KRI = 1/2m(arc KE).
Angle REI is an exterior angle of triangle KIR, so we have m∠REI = m∠ERK + m∠KRI.
To determine which angles must be right angles, we need to look for cases where the intercepted arcs are semicircles, which have a measure of 180 degrees.
If arc EIK is a semicircle, then m(arc EIK) = 180 and m∠ERK = 1/2(180) = 90. Therefore, angle ERK is a right angle.
If arc KE is a semicircle, then m(arc KE) = 180 and m∠KRI = 1/2(180) = 90. Therefore, angle KRI is a right angle.
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16 students at a school were asked about their favorite pasta dish. A graph of the results is on the left.
Create a bar graph showing the possible results for all 400 students in the school. Be sure to number the vertical axis.
Answer:
Step-by-step explanation:
to solve this question, we need to use the graph on the left to find the proportions of students who prefer each pasta dish, and then multiply those proportions by 400 to get the estimated number of students in the whole school who prefer each pasta dish. Then we need to plot those numbers on a bar graph with the pasta dishes on the horizontal axis and the number of students on the vertical axis. The graph below shows one possible way to create the bar graph:
We can see that the vertical axis is numbered from 0 to 120 in increments of 20. The bars show the estimated number of students who prefer each pasta dish, based on the sample of 16 students. For example, since 4 out of 16 students prefer spaghetti, we can estimate that 4/16 x 400 = 100 students in the whole school prefer spaghetti. Similarly, since 3 out of 16 students prefer lasagna, we can estimate that 3/16 x 400 = 75 students in the whole school prefer lasagna. We can repeat this process for the other pasta dishes and plot them on the graph.
✧☆*: .。. Hope this helps, happy learning! (*✧×✧*) .。.:*☆
Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft
The volume of the given cone is 402.1 cubic feet if the slant height is 10ft and the length is 6ft.
To calculate the volume of a cone, the formula used is :
V = (1/3) * π * [tex]r^2[/tex] * h
Here, the radius is the unknown term. we need to calculate the radius of the cone. We can use the Pythagorean theorem to find the radius of the cone.
[tex]l^2 = r^2 + h^2[/tex]
[tex]10^2 = r^2 + 6^2[/tex]
[tex]r = \sqrt{(10^2 - 6^2)}[/tex]
radius = 8 ft
V = (1/3) * π * [tex]r^2[/tex] * h
V = (1/3) * π *[tex]8^2[/tex] * 6
V = (1/3) * π * 384
V = 402.1 cubic feet
Therefore we can infer that the volume of the given cone is 402.1 cubic feet.
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The complete question is:
'Find the volume of this cone. Round to the nearest tenth.
slant height = 10ft
length = 6ft
Cîte numere de trei cifre se pot alcătui din cifrele 1, 2, 3, 4 încît:1) cifrele să nu se repete;2) cifrele să se repete.
There are 24 three-digit numbers without repeating digits, and 64 three-digit numbers with repeating digits.
How many three-digit numbers can be formed?1) Pentru a alcătui numere de trei cifre în care cifrele să nu se repete, putem utiliza principiul combinatoric al permutărilor. Având la dispoziție cifrele 1, 2, 3 și 4, vom avea 4 posibilități pentru a alege prima cifră, 3 posibilități pentru a alege a doua cifră și 2 posibilități pentru a alege a treia cifră. Prin înmulțirea acestor numere, obținem:
4 * 3 * 2 = 24
Există deci 24 de numere de trei cifre în care cifrele nu se repetă, utilizând cifrele 1, 2, 3 și 4.
2) Pentru a alcătui numere de trei cifre în care cifrele se repetă, vom avea 4 posibilități pentru a alege oricare dintre cele trei cifre și anume 1, 2, 3 și 4. Prin urmare, avem:
4 * 4 * 4 = 64
Există 64 de numere de trei cifre în care cifrele se pot repeta, utilizând cifrele 1, 2, 3 și 4.
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Here is a data set: 51, 47, 48, 51, 50, 8
Answer true or false for the following statements.
If you remove the outlier: 8
- the range will stay the same: false
- the mean will decrease: false
- the median will increase: true
The statements are classified as follows:
- the range will stay the same: false- the mean will decrease: false- the median will increase: true.How to obtain the features of the data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
8 is a low outlier, hence it is a value lower than the mean, meaning that the mean increases if we remove the observation of 8.
The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus if we remove the low value of 8, the next low value is of 47, meaning that the range decreases.
The ordered data-set is given as follows:
8, 47, 48, 50, 51, 51.
The data-set has an even cardinality of 6, hence the median is calculated as the mean of the two middle elements as follows:
Median = (48 + 50)/2
Median = 49.
Removing 8, the data-set is given as follows:
47, 48, 50, 51, 51.
Hence the median increases, as it will be the middle value of 50.
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From a Word Problem
An online camera store charges $3 for every
8x10 picture that you order. The
shipping cost is $8. Write an equation to
model this situation. How much will it cost to
get 5 pictures printed?
Tom is considering opening a pool cleaning business as a summer job, he wants to determine the percentage of people in his town that own a pool. which is the best group of people for tom to survey?
The best group of people for Tom to survey would be homeowners in his town, as they are more likely to have a pool in their backyard.
To determine the percentage of people in his town that own a pool, Tom should survey a random sample of residents within the town. This will help him gather accurate and representative data about pool ownership in the area for his potential pool cleaning business.
Tom can also narrow down his survey to neighborhoods that are known to have a higher concentration of pool owners. This will give him a more accurate percentage of pool owners in his town and help him make an informed decision about opening a pool cleaning business.
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450 cubic centimetres of wood is used to make a solid cylindrical ornament. the radius of the base of the ornament is 5 centimetres. what is the height of the cylindrical ornament? (formula = π x radius² x height)
a) 4.5 cm
b) 5.7 cm
c) 6.3 cm
d) 7.5 cm
The height of the cylindrical ornament is approximately 5.7 centimetres (option b).
To find the height of the cylindrical ornament given that 450 cubic centimetres of wood is used and the radius of the base is 5 centimetres, you can use the formula for the volume of a cylinder: V = π × radius² × height.
Step 1: Write down the given values.
Volume (V) = 450 cubic centimetres
Radius (r) = 5 centimetres
Step 2: Plug the given values into the formula.
450 = π × (5)² × height
Step 3: Solve for the height.
450 = π × 25 × height
450 = 78.54 × height
Step 4: Divide both sides by 78.54 to find the height.
height = 450 / 78.54
height ≈ 5.7 centimetres
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HELPPPP!!!!!!
Based on this information, which function best models the number of game consoles sold in millions x years since 2010?
A) g(x) = 20(1. 5)
B) g(x) = 0. 15(20)*
C) g(x) - 0. 150. 2)*
D) g(x) = 2000. 15)
The function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20).
To answer this question, we need to identify the function that best models the number of game consoles sold in millions x years since 2010.
Option A can be simplified to g(x) = 30, which is a constant function. This means that it does not depend on the value of x and is not a good model for the number of game consoles sold over time.
Option B can be simplified to g(x) = 3x, which is a linear function. This means that the number of game consoles sold increases at a constant rate over time. This could be a good model for the number of game consoles sold, but we need to compare it to the other options.
Option C can be simplified to g(x) = 0.03x, which is also a linear function. However, the rate of increase is much slower than in option B. This is not a good model for the number of game consoles sold.
Option D can be simplified to g(x) = 300, which is a constant function like option A. Again, this is not a good model for the number of game consoles sold over time.
Therefore, the function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20). This is a linear function that represents a constant rate of increase in the number of game consoles sold over time.
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complete question:
Based on this information, which function best models the number of game consoles
sold in millions x years since 2010?
A- g(x) = 0.15(20)^x
B- g(x) = 20(0.15)^x
C- g(x) = 20(1.5)^x
D- g(x) = 0.15(.2)^x
The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 925 among its requirements, what percentage of females do not satisfy that requirement?
The percentage of females who do not satisfy the minimum score requirement of 925 on the SAT-I test is 35.9%.
Calculating the z-score for the minimum score requirement:
z = (X - Mean) / Standard Deviation
z = (925 - 998) / 202
z = -73 / 202 ≈ -0.361
Now, using the z-score to find the percentage of females below the minimum score:
Since the z-score is -0.361, we can use a z-table (or an online calculator) to find the area to the left of this z-score, which represents the percentage of females who scored below 925. The area to the left of -0.361 is approximately 0.359.
3. Convert the area to a percentage:
Percentage = Area * 100
Percentage = 0.359 * 100 ≈ 35.9%
So, approximately 35.9% of females do not satisfy the minimum score requirement of 925 on the SAT-I test.
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3. What is the range of the functiony = 3x + 1 for
the domain 2 ≤ x ≤ 67
6 ≤ y ≤ 18
sy≤2
7 ≤ y ≤ 19
1
5
sys 3
The function f(x) models the height in feet of the tide at a specific location x hours after high tide.
f(x) = 3.5 cos (π/6 x) + 3.7
a. What is the height of the tide at low tide?
b. What is the period of the function? What does this tell you about the tides at this location?
c. How many hours after high tide is the tide at the height of 3 feet for the first time?
a) The height of the tide at low tide is 3.7 feet.
b) The period of the function is 12 hours and it means that the tide goes through a full cycle of high tide.
c) The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.
a. To find the height of the tide at low tide, we need to find the minimum value of the function f(x).
Since cos(π/6 x) has a maximum value of 1 and a minimum value of -1, the minimum value of the entire function occurs when cos(π/6 x) = -1.
This happens when π/6 x = π + 2nπ, where n is any integer.
Solving for x, we get x = 12 + 12n.
Substituting this value of x into the function, we get f(x) = 0 + 3.7 = 3.7 feet.
b. The period of the function is the time it takes for the function to complete one full cycle. Since the period of cos(π/6 x) is 2π/π/6 = 12 hours, the period of the entire function f(x) is also 12 hours. This means that the tide goes through a full cycle of high tide and low tide every 12 hours at this location.
c. To find the first time the tide reaches a height of 3 feet, we need to solve the equation 3 = 3.5 cos (π/6 x) + 3.7 for x.
Subtracting 3.7 from both sides and dividing by 3.5, we get cos(π/6 x) = -0.086.
Taking the inverse cosine of both sides, we get π/6 x = 1.67 + 2nπ or π/6 x = -1.67 + 2nπ, where n is any integer.
Solving for x, we get x = 40.18 + 24n or x = 23.82 + 24n.
The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.
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Select all of the statements that are true.
Previous question
The 9.7-9.7 because the distance from -9.7 to 0 on the number line is 9.7 units.
Numbers with the same absolute value are opposites because they are the same distance from each other.
The 7.1 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units.
The -8.4 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units.
=
Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line.
The -12.5 12.5 because the distance from 12.5 to 0 on the number line is -12.5 units.
N
The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.
b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.
c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.
d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.
e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.
Therefore, the correct statements are b, c, and e.
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If x = -3, then which inequality is true?
The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0
If x = -3, then which inequality is true?From the question, we have the following parameters that can be used in our computation:
The statement that x = -3
The above value implies that we substitute -3 for x in an inequality and solve for the variable y
Take for instance, we have
y < x + 3
Substitute the known values in the above equation, so, we have the following representation
y < -3 + 3
Evaluate
y < 0
This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0
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She wants to play cornhole, but she does not have enough pink bean bags
with her set. However, Sarah keeps a box of spare bean bags in her garage. If
the box contains one yellow, four blue, three red and two pink bean bags,
what is the probability to the nearest tenth of a percent that she will select
the two pink bean bags from the box on her first two attempts?
The probability that she will select the two pink bean bags from the box on her first two attempts is approximately 2.2%.
To calculate the probability that she will select the two pink bean bags from the box on her first two attempts, we need to;
1. Determine the total number of bean bags in the box. There is one yellow, four blue, three red, and two pink bean bags, which makes a total of 1 + 4 + 3 + 2 = 10 bean bags.
2. Calculate the probability of selecting a pink bean bag on the first attempt. There are two pink bean bags out of 10, so the probability is 2/10 or 1/5.
3. After selecting one pink bean bag, there are now nine bean bags left in the box. Calculate the probability of selecting the second pink bean bag on the second attempt. Since there is only one pink bean bag left, the probability is 1/9.
4. To find the overall probability of selecting two pink bean bags in the first two attempts, multiply the probabilities from steps 2 and 3. So, the probability is (1/5) * (1/9) = 1/45.
5. Convert the fraction to a percentage by dividing the numerator by the denominator and multiplying by 100. (1/45) * 100 = 2.22% (rounded to the nearest tenth of a percent).
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Which of the following are areas of sectors formed by Angle ABC?
B = 86.4º
AB=4.1cm
Answer:
about 12.67 cm²
Step-by-step explanation:
The area of a sector of a circle is given by:
A = (θ/360) x πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
In this case, we are given the central angle of the sector, which is 86.4 degrees, and the radius of the circle, which is 4.1 cm. Therefore, we can calculate the area of the sector formed by angle CBA as follows:
A = (86.4/360) x π(4.1)²
A ≈ 12.67 cm²
So, the area "about 12.67 cm²" is a possible area of the sector formed by angle CBA.
To determine if any of the other given areas are possible, we can calculate the central angle of each sector using the same formula as above, and then check if it matches the given angle of 86.4 degrees.
For the area "about 23.35 cm²":
23.35 = (θ/360) x π(4.1)²
θ ≈ 149.6 degrees
The central angle of this sector is approximately 149.6 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 23.35 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 3.09 cm²":
3.09 = (θ/360) x π(4.1)²
θ ≈ 19.16 degrees
The central angle of this sector is approximately 19.16 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 3.09 cm²" is not a possible area of the sector formed by angle CBA.
For the area "about 40.14 cm²":
40.14 = (θ/360) x π(4.1)²
θ ≈ 256.4 degrees
The central angle of this sector is approximately 256.4 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 40.14 cm²" is not a possible area of the sector formed by angle CBA.
Therefore, the only possible area of the sector formed by angle CBA is "about 12.67 cm²".
A person completes 68 km in 50 minutes via Jeep. Starting 20 minutes, he travels by x km/hr and
next 25 minutes by 2x km/hr and rest time by 3x km/hr. What is the value of x ?
The value of x is 48 km/hr.
How to solve for X
Total distance = 68 km
Total time = 50 minutes
First part:
Duration = 20 minutes
Speed = x km/hr
Second part:
Duration = 25 minutes
Speed = 2x km/hr
Third part:
Duration = 50 - (20 + 25) = 5 minutes
Speed = 3x km/hr
We can calculate the distance traveled in each part using the formula:
distance = speed × time
For the first part:
distance1 = x × (20/60) = (1/3)x (because 20 minutes = 1/3 hour)
For the second part:
distance2 = 2x × (25/60) = (5/6)x (because 25 minutes = 5/12 hour)
For the third part:
distance3 = 3x × (5/60) = (1/4)x (because 5 minutes = 1/12 hour)
Now, we know that the total distance is 68 km, so:
distance1 + distance2 + distance3 = 68
(1/3)x + (5/6)x + (1/4)x = 68
To solve for x, we'll first find a common denominator for the fractions, which is 12:
(4/12)x + (10/12)x + (3/12)x = 68
Now, add the fractions:
(4+10+3)/12 * x = 68
17/12 * x = 68
To isolate x, we'll multiply both sides by the reciprocal of the fraction (12/17):
x = 68 * (12/17)
x = 4 * 12
x = 48
So, the value of x is 48 km/hr.
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