Answer:
P(A and B) = 0.25
Step-by-step explanation:
Since P(A) and P(B) are independents events, The probability P(A) and P(B) occurs consecutively is P(A)*P(B):
P(A and B) = P(A)*P(B)
P(A and B) = 0.512*0.488
P(A and B) = 0.25
Two trains for Palwal leave Kanpur at 10 am and 10:30 am and travel at the speeds of 60Kmph and 75Kmph respectively. After how many kilometers from Kanpur will the two trains be together?
Answer:
150 km
Step-by-step explanation:
You want to know the number of kilometers each train has traveled when they meet. The first goes 60 km/h and has a half-hour head start. The second goes 75 km/h.
SetupAt t hours after 10 am, the distance of the first train from Kanpur will be ...
distance = speed × time
distance = 60t
At t hours after 10 am, the distance of the second train from Kanpur will be ...
distance = 75(t -1/2) . . . . . . the distance is 0 at 10:30 am, 1/2 after 10 am
These distances will be equal when ...
60t = 75(t -1/2)
SolutionThe time at which the trains meet will be the solution to the above equation.
60t = 75t -37.5 . . . . eliminate parentheses
0 = 15t -37.5 . . . . . . subtract 60t
0 = t -2.5 . . . . . . . . . divide by 15
2.5 = t . . . . . . . . . the trains meet 2.5 hours after the first one leaves
The distance traveled by each of the trains is the same at that time. It will be the distance traveled by the first train:
60t = 60(2.5) = 150 . . . . km
The two trains will be together 150 km from Kanpur.
What is 1/8 as a Decimal
RCX)=2VX SCx) = x(RSX4=
Given the two functions:
[tex]\begin{gathered} R(x)=2\sqrt[]{x} \\ S(x)=\sqrt[]{x} \end{gathered}[/tex]We need to find (RoS)(4). THis is the functional composition. We take S(x) and put it into R(x) and then put "4" into that composed function. Shown below is the process:
[tex](RoS)(x)=2\sqrt[]{\sqrt[]{x}}[/tex]When we plug in "4", into "x", we have:
[tex]\begin{gathered} (RoS)(x)=2\sqrt[]{\sqrt[]{x}} \\ (RoS)(4)=2\sqrt[]{\sqrt[]{4}} \\ =2\sqrt[]{2} \end{gathered}[/tex]2.Graph and complete the t-chart for the function y=2/3 x +5.
Recall that to complete the table we have to evaluate the given function at every value of x:
[tex]\begin{gathered} y(-3)=\frac{2}{3}(-3)+5=-2+5=3, \\ y(3)=\frac{2}{3}(3)+5=2+5=7, \\ y(6)=\frac{2}{3}(6)+5=4+5=9. \end{gathered}[/tex]Answer:
Table:
Graph:
5. Given the following lengths, determine if the shape is a RIGHT triangle: 14, 16, 18 (2 points: 1 point for the correct answer, 1 point for showing your work) Your answer
To be able to determine if the figure is a right triangle.
The given length must satifies the given conditions,
a.) The sum of the two sides must always be lesser than the other side. We get,
[tex]\text{ a + b }>\text{ c ; b+ c }>\text{ a ; a + c }>b[/tex]Given: a = 14 ; b = 16 ; c = 18
Let's check,
a + b > c ; 14 + 16 > 18 = 30 > 18 Satisfies the criteria
b + c > a ; 16 + 18 > 14 = 34 > 14 Satisfies the criteria
a + c > b ; 14 + 18 > 16 = 32 > 16 Satisfies the criteria
b.) The square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem). We get,
[tex]\begin{gathered} \text{ c}^2=a^2+b^2 \\ 18^2=14^2+16^2 \\ 324\text{ = }196\text{ + }257 \\ 324\text{ }\ne\text{ 457} \end{gathered}[/tex]Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.
Use the number line to find the coordinate of the midpoint of
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.
Juan rides the bus to school each day. He always arrives athis bus stop on time, but his bus is late 80% of the time.Juan runs a simulation to model this using a randomnumber generator. He assigns these digits to the possibleoutcomes for each day of the week:• Let 0 and 1 = bus is on time• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is lateThe table shows the results of the simulation.
B. 2/10 = 20%
Explanations:The total number of weeks shown in the simulation = 10
By observing the simulation, we would see that there is no 0 or 1 in group 2 and group 3. This means that Juan was late everyday of week 2 and week 3
The number of weeks that Juan was late everyday = 2
The estimated probability that Juan will be late evryday of next week = 2/10 = 20%
Given f(x) = ln(x), which is the correct answers ?
First, lets perform each transformation and then take a look at its graph:
1.
[tex]\begin{gathered} g(x)=-\frac{1}{2}f(x-2) \\ \\ \Rightarrow g(x)=-\frac{1}{2}\ln (x-2) \end{gathered}[/tex]The only etiquette that matches this plot is: Function decreases as x increases
2.
[tex]\begin{gathered} h(x)=f(x-\frac{1}{2}) \\ \\ \Rightarrow h(x)=\ln (x-\frac{1}{2}) \end{gathered}[/tex]The only etiquette that matches this plot is: x-intercept at (1.5 , 0)
3.
[tex]\begin{gathered} j(x)=f(x)-\frac{1}{2} \\ \\ \Rightarrow j(x)=\ln (x)-\frac{1}{2} \end{gathered}[/tex]The only etiquette that matches this plot is: Asymptote of x = 0
Find the area of this circle.Use 3.14 to approximate n.Α = πη28 inA = [ ? ] in?
To find the area of a circle given its radius,
[tex]\text{Area}=\pi\times r^2[/tex]The value of the radius r = 8 inches, and the value of pi is 3.14. Hence;
[tex]\begin{gathered} \text{Area}=3.14\times8^2 \\ \text{Area}=3.14\times64 \\ \text{Area}=200.96in^2 \end{gathered}[/tex]The area of the circle is 200.96 inches squared
Order from least to greatest5/6 4/50.82
Okay, here we have this:
Considering the provided set of numbers we are going to organize the numbers from smallest to largest, so we obtain the following:
Remember that 5/6 is approximately 0.83 and 4/5 is 0.8, then:
Considering the number line and that the smaller numbers are further to the left and the larger numbers are further to the right, we are left with the following order from least to greatest: 4/5, 0.82, 5/6.
Last year, Tammy opened an investment account with $8200 . At the end of the year, the amount in the account had decreased by 7.5% . How much is this decrease in dollars? How much money was in her account at the end of last year?
1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.
2. The balance in Tammy's investment account at the end of last year was $7,585.
What is the percentage?The percentage is the proportion of a value in relation to another.
Percentages show how much a variable is contained in another.
The percentage gives the fractional value of the decrease in the investment account.
Initial investment = $8,200
Decrease in investment = 7.5%
Decrease in dollars = $615 ($8,200 x 7.5%)
Balance = $7,585 ($8,200 - $615)
Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.
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help meeeeeee pleaseee !!!!
The linear equation that passes through the two points (0, 360) and (10, 560) is:
y = 20*x + 360
How to find the linear equation?Remember that the slope-intercept form of a linear equation is:
y = a*x + b
Where b is the y-intercept and a is the slope or rate of change.
If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
[tex]a = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
Here the line must pass through (0, 360) and (10, 560), so the slope is:
[tex]a = \frac{560 - 360}{10 - 0} = 20[/tex]
And because of the point (0, 360) we can see that the y-intercept is 360, then the linear equation is:
y = 20*x + 360
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Let's take a look at (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2). While Beeker believes that these two expressions are equal for all real numbers x and y Clod believes they are not! Let's get to the bottom of this!
a) Evaluate (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2) for x = 7 and y = 11
b) For which values of x and y does (x + y)^2 (x - y)^2 equal (x^2 + y^2)(x^2 - y^2)? For which values of x and y does (x + y)^2 (x - y)^2 not equal (x^2 + y^2)(x^2 - y^2)?
From the given expression, it is found that:
a) When x = 7 and y = 11, the numeric values are given as follows:
(x + y)²(x - y)² = 5184.(x² + y²)(x² - y²) = 12240.b) They will only have the same numeric value when x = y.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.
The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.
In the context of this problem, the expressions are given as follows:
(x + y)²(x - y)².(x² + y²)(x² - y²).When x = 7 and y = 11, the numeric values are given as follows:
(11 + 7)²(11 - 7)² = 5184.(11² + 7²)(11² - 7²) = 12240.The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.
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Calculate the mean of the electric bills for Family A. Round your answer to the nearest cent.
Month Family A Family C
January
February
March
April
May
June
July
August
September
October
November
December
$
Answer:
78.59$
Step-by-step explanation:
( – 5q–1)–( – 2q–8)
help meeeee
The value of expression ( – 5q–1)–( – 2q–8) is -3q + 7.
As per the known fact, the similar signs are consequently takes as positive for calculation. So, the two negative signs will be takes as positive. So, rewriting the expression to solve and find its value.
Value of expression = (-5q - 1) + 2q + 8
Rearrange the expression
Value of expression = - 5q + 2q - 1 + 8
Performing addition of numerals written with q and subtraction of constant values
Value of expression = - 3q + 7
Thus, the value of expression mentioned in question is -3q + 7.
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PLEASEEE HELP ME
find the inverse of f(x)=1/x+5 -1 and it’s domain
Answer:
C
Step-by-step explanation:
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The correct option is True, there is enough information given to say that both line are parallel.
What is termed as as the supplement angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.For the given question.
The two lines are given with angles measure from 1 to 8.
Where,
∠4 = 89°∠3 = 91°As, the sum of the angles is;
∠4 + ∠3 = 91° + 89°
∠4 + ∠3 = 180° (supplementary angles)
Thus, we can say that both lines are parallel to each other.
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The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is 5 cm. Find the length of the other leg. i think its 12
Answer: Correct! The answer is 12.
Step-by-step explanation:
1) Draw the triangle.
Drawing a triangle usually helps you see the problem better!
| \
| \ 13 cm
| \
|______\
5 cm
2) Solve the other leg
To find the other leg, we need to use the Pythagorean theorem. Which goes like this
[tex]a^2+b^2=c^2[/tex]
We will then substitute the numbers into the equation
[tex]5^2+b^2=13^2[/tex]
Simplify
[tex]25+b^2=169[/tex]
Set the variable on one side
[tex]b^2=144[/tex]
Get rid of the squared in the b by square rooting both sides.
[tex]b=12[/tex]
The answer is 12.
Solve 3x - 2y = - 6 if the domain is {-2, -1, 0, 2, 3).
Write your answer as ordered pairs.
The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.
Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,
At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.
These are the values of outputs, and the ordered pair will be expressed as
{0, 3/2, 3, 6, 15/2}.
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A football team has a 60% chance of winning a league trophy each season it competes. What would be its probability of winning two times in three consecutive seasons?
Answer:
P(X = 2) = 43.2%
Step-by-step explanation:
P(X = 2) = 3 * 0.6^2 * (1 - 0.6)^(3 - 2)
P(X = 2) = 54/125
P(X = 2) = 0.432
P(X = 2) = 43.2%
One ounce is 28.35 grams. Convert16 ounces into grams. Round to nearest tenth
16 ounces is equivalent to 453.6g when rounding to nearest tenth.
What is rounding off ?
Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.
To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.
here the given data is :
1 ounce = 28.35 grams
Conversion of ounce to grams :
This is the conversion of a mass unit from ounce to grams. Given that 1 ounce is equal to 28.35 grams, let us calculate how grams would be in 16 ounces.
The easiest way about this is simply multiply 16 by 28.25g
1 ounce = 28.35 grams
16 ounce = x
x = 16 x 28.25
x= 453.6 g
From the calculations above, 16 ounces is equivalent to 453.6g.
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A worker in an assembly line takes 7 hours to produce 31 parts. At that rate, how many parts can she produce in 28 hours?
Answer:
124
Step-by-step explanation:
Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.
[tex]31(4)=124[/tex]
In an apartment 40%read the nation 25%read the standard 5%read both .if a random resident is selected calculate the probability that
Astronomers discover an exoplanet (a planet of a star other than the Sun) that has an orbital period of 3.95 Earth years in its circular orbit around its sun, which is a star with a measured mass of 3.97×1030kg . Find the radius of the exoplanet's orbit.
The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.
How to calculate the radius of the exoplanet's orbit?In order to calculate the radius of the exoplanet's orbit, we would apply Kepler's Third Law of planetary motion.
Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:
T² = 2π√(r³/GM)
Where:
T represents the orbital period.M represents the mass.G represents the universal gravitational constant.r represents the radius.Making radius (r) the subject of formula, we have:
Radius, r = ∛(GMT²/2π)
Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².
Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds
Substituting the given parameters into the formula, we have;
Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)
Radius, r = 4.71 × 10¹¹ meters.
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5. Higher Order Thinking Linda wants to show
skip counting by 5s from a number to get to
1,000. Write the numbers she should put on
her number line below. How do you know?
1,000
The numbers that Linda should put on her number line are 5,10,15,20...1000 .
Integers are frequently represented as specifically labelled dots evenly spaced on a line. Despite the fact that the graphic only depicts the integers from -3 to 3, the product contains all real numbers, which continue indefinitely in each direction, as well as numbers that lie between the integers. It is frequently used to help teach simple numerals, particularly with negative numbers.
The numbers are skip counted. so each number differs from the preceding number by 5.
let us take the number counting starts from 0. so the second number will be 5+5=10
The third number 10+5 = 15 and so on and so forth.
Hence it forms an arithmetic sequence of numbers whose first term is 5 and common difference is 5.
A number line is really a picture of a stepped straight line as serves as a visual representation of real numbers in primary mathematics. Every point of a x axis is assumed to coincide to a true figure, and every decimal digits to a point.
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are all angles are congruent to one another
Answer:
Step-Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.
Find the height h of the solid. h I B = 147 cm2 Volume 1323 cm h= cm
Answer:
h = 9 cm
Explanation:
The volume of the solid can be calculated as:
[tex]V=B\cdot h[/tex]So, we can replace the value of the Volume by 1323 cm³ and B by 147 cm² as:
[tex]1323cm^3=147cm^2\cdot h[/tex]Then, dividing by 147 into both sides, we get:
[tex]\begin{gathered} \frac{1323cm^3}{147cm^2}=\frac{147cm^2\cdot h}{147cm^2} \\ 9\text{ cm = h} \end{gathered}[/tex]Therefore, the height h of the solid is 9 cm.
Please!!Find the value of each variable. Write theequations and solve showing ALL the work.If an answer is not a whole number, leaveit in simplest radical form.
The greater triangle and the smaller ones (the two triangles inside the original one, that share the side y) are similar triangles, then we can formulate the following expressions:
• For the larger triangle and the triangle on the left
[tex]\frac{z}{9}=\frac{5}{z}[/tex]From this equation, we can solve for z, to get:
[tex]\begin{gathered} \frac{z}{9}\times z=\frac{5}{z}\times z \\ \frac{z\times z}{9}=5\times\frac{z}{z} \\ \frac{z^2}{9}=5\times1 \\ \frac{z^2}{9}=5 \\ z^2=5\times9 \\ z^2=45 \\ z=\sqrt[]{45} \\ z=3\sqrt[]{5} \end{gathered}[/tex]Then, z equals 3√5
• Similarly, with the larger triangle and the one on the right:
[tex]\begin{gathered} \frac{x}{9}=\frac{4}{x} \\ \end{gathered}[/tex]From this expression, we can solve for x, like this:
[tex]\begin{gathered} \frac{x}{9}=\frac{4}{x} \\ \frac{x^2}{9}=4 \\ x^2=4\times9 \\ x^2=36 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}[/tex]Then, x equals 6
• With the triangles on the right and on the left:
[tex]\frac{y}{4}=\frac{5}{y}[/tex]Solving for y, we get:
[tex]\begin{gathered} \frac{y}{4}=\frac{5}{y} \\ \frac{y^2}{4}=5 \\ y^2=5\times4 \\ y^2=20 \\ y=\sqrt[]{20} \\ y=2\sqrt[]{5} \end{gathered}[/tex]Then, y equals 2√5
find the perimeter of the hallway
Answer: 17x - 39
Step-by-step explanation:
1) Find all sides of the hallway.
P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1
2) Add it together
P= 17x - 39
HELP I DONT UNDERSTAND THEIS QUESTIIONS
1) f(x)-3
[tex]\begin{gathered} f(x)=2x-4 \\ \Rightarrow f(x)-3=2x-4-3 \end{gathered}[/tex]Therefore, f(x)-3=2x-4-3
2) f(x-3)
[tex]\Rightarrow f(x-3)=2(x-3)-4[/tex]Thus, f(x-3)=2(x-3)-4
3) f(-3x)
[tex]f(-3x)=2(-3x)-4[/tex]Then, f(-3x)=2(-3x)-4
4) -3f(x)
[tex]-3f(x)=-3(2x-4)[/tex]Hence, -3f(x)=-3(2x-4)