1 The probability of no cars crossing the road in this time interval is given by P(N = 0) = e^(-λ)λ^0/0! = e^(-6) ≈ 0.00248.
2 The expected time of occurrence of the fifth car after 2 P.M. is 5/3 hours, or 1 hour and 40 minutes, after 2 P.M.
The number of cars that cross the road between 8 and 10 in the morning can be modeled by a Poisson distribution with parameter λ = AΔt = 3 cars/hour × 2 hours = 6 cars. The probability of no cars crossing the road in this time interval is given by P(N = 0) = e^(-λ)λ^0/0! = e^(-6) ≈ 0.00248.
The time between successive cars crossing the road is exponentially distributed with parameter λ = 3 cars/hour. Thus, the expected time of occurrence of the fifth car after 2 P.M. can be calculated as the sum of the expected times between the fourth and fifth cars, the third and fourth cars, and so on, up to the first and second cars. Each expected time is equal to 1/λ = 1/3 hour.
Therefore, the expected time of occurrence of the fifth car after 2 P.M. is 5/3 hours, or 1 hour and 40 minutes, after 2 P.M.
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What are the 5 types of math?
Algebra
Geometry
Trigonometry
Calculus
Statistics and Probability
Hope it Helps!
The point (2,−3) lies in the third quadrant.ATrueBFalse
Answer:
B. False
Pont (2, -3) lies on the fourth quadrant.
Step-by-step explanation:
You're welcome.
Find the missing values in the ratio table. Then write the equivalent ratios in the order they appear in the table.
Flour (cups)
Oats (cups)
So, 30 and 5 are the values that are missing is calculated by ratio and proportion.
What are prop and ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
If both the antecedent and the consequent are multiplied or divided by the same non-zero number, the ratio remains the same.
i.e.,
We can see from the provided table that:
In the second column,
Since, 6x0.5=3
Thus, multiply 10 by the same number.
10x0.5=5
For the third column,
since,
50=10x5
multiply by the same number, then
6x5=30
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-Ready
Distance in the Coordinate Plane-Quiz - Level F
Which expression represents the distance
between point J and point K?
|-9|-|-2| |-9|+|-2|
|6|-|-2|
|6|+|-9|
-10
10 y
0
-10
-J (6,-2).
K (6,-9).
I
10
X
The required distance between the points J and K is given as D = √113.
What is Distance?Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
Two points, J and K have the coordinates (6,-2). and K (6,-9).
Distance between the point is given by the distance formula.
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
D = √{6 + 2}² + {-9 + 2}²
D= √64+ 49
D = √113
Thus, the required distance between the points J and K is given as D = √113.
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-2.75x + 7 = -26
Show work
Answer:
This is a simple algebraic equation, it can be solved by isolating the variable on one side of the equation.
-2.75x + 7 = -26
Add 26 to both sides of the equation:
-2.75x + 33 = 0
Divide both sides by -2.75:
x = -12
So the solution of the equation is x = -12.
Note that x = -12 is the value of x that makes the equation true
Answer:
x = 12
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 12
12.) There are 12 cats and 13 dogs in math class. What percent of the class are cats?
Answer:
48%
Step-by-step explanation:
You want to know the percent of the class that is cats if there are 12 cats and 13 dogs in the class.
PercentThe percent can be found by multiplying the fraction by 100%.
cats/class = 12/(12+13) × 100% = 12/25 × 100% = 48%
48% of the class are cats.
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what are the bionomial factors of the polynomial x^3-5x^2+2x+8
Answer:
[tex](x+1)(x-2)(x-4)[/tex]
Step-by-step explanation:
By the Rational Root Theorem, possible rational solutions for the given polynomial are [tex]\pm1,\pm2,\pm4,\text{ and}\pm8[/tex], so we can test each one:
1 | 1 -5 2 8
____ 1_-4_-2
1 -4 -2 | 6 <-- (x-1) IS NOT a root
-1 | 1 -5 2 8
____-1_ 6_ -8
1 -6 8 | 0 <-- (x+1) IS a root
So, [tex]x^3-5x^2+2x+8=(x+1)(x^2-6x+8)=(x+1)(x-2)(x-4)[/tex]
Juanita heard a funny joke on Sunday. On Sunday, she told the joke to 3 friends. On Monday, each friend told the joke to 3 more friends. On Tuesday, these 3 friends told the joke to 3 more friends. Suppose this pattern continues. How long will it take for 100 people to hear the joke?
Answer:
9 × x = 100
x = 11
Therefore, it would take 11 more days.
Need help with this question
On solving the question, we can say that rounded to the nearest tenth, trigonometry is 94.7.
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations.
To find the length of TR, we can use the ratio of similarity between the two triangles. Since triangle NOP is similar to triangle RST, we know that the ratio of the corresponding sides is equal. In this case, we can set up the proportion:
(TR)/(NO) = (TS)/(OP)
We know that NO = 34 and OP = 19, and we are trying to find TR. We also know that TS = 60. We can set up the proportion and solve for TR:
(TR)/34 = 60/19
TR = (60/19) * 34
TR = 94.73
Rounded to the nearest tenth, TR is 94.7.
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Proportional or nonproportional? Need answer asap
Answer:
Proportional
Step-by-step explanation:
Okay so let's do this problem. In order to figure this out we must find if the slope remains the same.
For y
61-26= 35 26-11= 15
For x
12-5= 7 5-2= 3
35/7 = 5
15/3 = 5
Since the slope remains 5 between the three points this is proportional.
How do you write the symbol for greater than 1?
The symbol for greater than 1 is written as " >1".
Greater than ">" means that one number or value is larger than the other. number or value The symbol is made by your right-hand thumb and index finger, just like ">", which is known to be a "greater than" symbol. If you use this symbol to write some value is greater than 1 then you need to write 1 towards the right side of this symbol.
For example, 9 > 1. The open end of the greater than symbol is pointed at the one and it is read as '9 is greater than 1. So the symbol for any value greater than 1 is written as " >1".
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In △ABC , point D lies on AC¯¯¯¯¯¯¯¯ , point E lies on BC¯¯¯¯¯¯¯¯ , and DE¯¯¯¯¯¯¯¯∥AB¯¯¯¯¯¯¯¯ .
The value of the ratio OC'' : OC' is given as follows:
OC'' : OC' = 1 : 4.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
For point C', the scale factor is given as follows:
k = 2.
For point C'', the scale factor is given as follows:
k = 1/2.
The ratio between two amounts a and b is given by the division of a and b, as follows:
a : b.
Hence the ratio between the distances OC'' and OC' is given as follows:
(1/2)/2 = 1/2 x 1/2 = 1/4.
(division of fractions, we multiply the first fraction, of 1/2, by the inverse of the second fraction 2/1, which is of 1/2).
In ratio notation, we have that:
OC'' : OC' = 1 : 4.
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What are the three types of coordinates?
The three types of co-ordinates are:
(i) Cartesian co-ordinates
(ii) cylindrical co-ordinates
(iii) spherical co-ordinates
Which coordinate system is used?Three digits are used to indicate distances in the three-dimensional flat space of the Cartesian coordinate system, often known as the "rectangular coordinate system." The East/West direction, North/South direction, and Elevation are represented by the first two digits, respectively.
The Cartesian coordinate system is a prime example of a coordinate system. Two perpendicular lines are picked in the plane, and a point's coordinates are assumed to be the signed distances between the lines.
So, three types of co-ordinates are:
(i) Cartesian co-ordinates
(ii) cylindrical co-ordinates
(iii) spherical co-ordinates
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What is the angle measure of x? (numbers only)
Answer:30 degrees
Step-by-step explanation:
S = O/H
sin-1(6/12) = 30
find the measure of each angle indicated
Answer:
Use the formula sum of internal angles of a triangle is 180
in a school 21% of teachers were trained in britain and 26% of teachers were trained in usa and 15% were trained in both Britain and USA what percentage of teachers were neither trained in usa nor Britain represent using a venn diagram
A Venn diagram to represent the given information of a school and attached
The percentage of the teachers neither trained in USA or Britain is 68%
How to find the percentage of the teachers neither trained in USA or BritainSince the problem is stated in percentage, the total number of teachers in the school which is the universal set is 100
15% were trained in both Britain and USA.
The number of teachers trained in Britain only
= 21% - 15% = 6%
The number of teachers trained in USA only
= 26% - 15% = 11%
The total number of teachers trained in Britain and USA
= number of teachers trained in Britain only + number of teachers trained in USA only + number of teachers trained both Britain and USA
= 6% + 11% + 15%
= 32%
percentage of the teachers neither trained in USA or Britain
= universal set - number of teachers trained in Britain and USA
= 100% - 32%
= 68%
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Which of the following is not equivalent to the other three?
a.
sin x
sinx
C.
tan x
1– cosx'1+cosx
secx-1
b. 2 cotx sec x
d.
A
B
C
D
Please select the best answer from the choices provided
+
sin x
1- sin x
tanx
secx + 1
+
sin x
1+ sin x
On solving the question, the answer of given trigonometric question is tanx-sinx.
Is trigonometry challenging?This is due to the fact that trigonometry is still regarded as a very challenging and abstract branch of mathematics in comparison to other branches. When learning trigonometry, students frequently run into mistakes, misunderstandings, and barriers. A subfield of mathematics known as trigonometry studies how angles and length ratios relate to one another. Applications of geometry to astronomical research led to the field's emergence in the Hellenistic civilization during the third century BC.
cosecx(secx−1)−cotx(1−cosx)
= 1/sinx*1(1-cosx)/sinxcosx−cosx(1−cosx)/sinx
=((1−cosx)−sinxcosx(1−cosx))/sinxcosx
=sinxcosx(1−cosx)−cos^2x(1−cosx)
=(1−cosx)(1−cos2x)/sinxcosx
=(1−cosx)×sin2^x/sinxcosx
=tanx(1−cosx)
=tanx−tanxcosx
=tanx−sinx/cosx×cosx
=tanx−sinx
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Explain why the initial value of any function of the form f(x) = a(bx) is equal to a
In the function f(x) = a(b^x), the initial value is always a because a is independent on x. So, when x changes, b^x will change as well but a will remain the same.
How to explain the function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. A function is an equation with a single solution for y for each value of x. A function pairs each input of a particular type with exactly one output.
For example, let a = 2, b = 3, and x = 0: f(0) = 2 3^0 = 2 1. If x = 1, then f(1) = 2 3^1 = 2 3. If x = 2, then f(2) = 2 3^2 = 2 9, etc. As you can notice a = 2 remain unchanged as the initial value, because a is independent on x change.
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it takes Maria 340 seconds to travel 4400 meters in her car.what is her rate of speed in kilometers per hour?please answer ASAP:)
Answer:
Takes maria
Step-by-step explanation
Maria's rate of speed is 46.5 kilometers per hour.
What is the distance?
Distance is defined as the product of speed and time.
Since there are 3600 seconds in an hour, we can divide the time it takes Gretchen to travel 4400 meters by 3600 to find the number of hours it takes her:
⇒ 340 seconds / 3600 seconds/hour = 0.09444444 hours.
Next, we need to convert the distance she travels to kilometers. Since there are 1000 meters in a kilometer, we can divide the distance Maria travels by 1000 to find the number of kilometers she travels:
⇒ 4400 meters / 1000 meters/kilometer = 4.4 kilometers.
Now that we have the distance Maria travels and the time it takes her to travel that distance in the appropriate units, we can divide the distance by the time to find her rate of speed in kilometers per hour:
⇒ 4.4 kilometers / 0.09444 hours = 46.5882375 kilometers/hour.
Thus, Maria's rate of speed is 46.6 kilometers per hour.
How much interest will Hannah earn in four years if she deposit $630 in a savings account at 6.5% simple interest?
$93.60
Step-by-step explanation:Simple interest shows the amount of money an account earns based on the initial deposit.
Interest Formula
The formula to find the amount of interest earned is I = Prt. In this equation, I is the total interest earned, P is the principal or the initial deposit, r is the interest rate as a decimal, and t is the time in years.
To find the total balance of the account just add the interest amount to the principal. So, A = I + P, where A is the total balance.
Solving for Simple Interest
For this question, the variables are:
P = 630r = 0.065t = 4Now, we can plug these values into our formula.
I = 360 * 0.065 * 4I = 93.6After 4 years, the account will earn $93.60 in simple interest.
What is the example of cardiovascular fitness and body composition?
Jogging, cycling, swimming, aerobics, rowing, stair climbing, and sports-related games are examples of cardiovascular fitness. For Body composition, the push-up is the best example.
During a physical activity like running, jogging, or doing workouts involving cardiovascular activities, the circulatory and respiratory systems of the body provide oxygen to the skeletal muscles. When oxygen reaches the muscles, the risk of cardiovascular disease is decreased.
Also, the body is able to do larger muscle exercises due to increased flexibility, and the efficiency of the respiratory system also increases. But more blood is pumped through the body due to cardiorespiratory activities is not the benefit of doing physical activities.
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Write the inequality represented on each graph. Use n for the variable.
Graph 1 has n<14 inequalities, and graph 2 has n>14 inequalities.
What exactly is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another.
The two rules of inequality :
Rule 1: Adding or subtracting the same amount from both sides of an inequality does not change the inequality symbol. Rule 2: Multiplying or dividing both sides by a positive number does not change the inequality symbol.
Here graph 1 depicts
The line is extending to the left of the number 14, excluding 14.
So, the inequality will be;
n < 14.
The graph 2 depicts
The line, which includes the number 14, is moving to the right.
So, the inequality will be ;
n≥14
As a result, the inequalities are n14 and n14 of graphs 1 and 2, respectively.
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Which is a solution of the equation 7x 5/19 * 1 point?
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here, the formula is written as x3 -10x = 100.
We continue testing for the value of x that is valid for x3 -10x = 100 via trial and error.
We've made multiple tries and have:
x = 5.4 (roughly) (approximately)
In x3 -10x = 100, replace x with 5.4.
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
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On solving the provided question, we can say that the equation, we have here is 7x + 5/19 => 7x = -5/19 = > x = -5/133
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation, we have here is
7x + 5/19
7x = -5/19
x = -5/133
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What is the coefficient of y² in the expression 3y² 4x *?
3 is the coefficient of y² in the expression 3y²+4x
What is the term for coefficient?A coefficient is an integer that is either printed alongside or multiplied by a variable. A coefficient, in other terms, is the numerical component of a phrase including constants and variables. For example, the coefficient in the expression 2x is 2. A coefficient is a number that has been multiplied by a variable. Coefficient examples: The coefficient in the expression 14 c 14c 14c is 14. The coefficient in the phrase g is 1.
In an expression, it is generally a number, although it may also be a letter. In the phrase ax2 + bx + c, for example, x is the variable and ‘a’ and ‘b’ are the coefficients.
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Hideki buys 2 sweaters for $18 each. He can use one of the following coupons :
Coupon 1: Buy one, get one 40% off
Coupon 2: 25% off entire purchase
Which coupon should Hideki use to get a better deal?
The coupon which gives Hideki a better deal is Coupon 2: as the total cost is: $27
The total cost of coupon 1 will be; $28.8
The total cost of coupon 2 will be; $27
For Coupon 1; Buy 1 get one 40% off.
Total cost = $18 + 60% ($18)
Total cost = $18 + $10.8.
Total cost = $28.8
For Coupon 2; 25% off entire purchase
Total cost = 75% ($18 + $18)
Total cost = 75% ($36)
Total cost = $27
:D Your Welcome!
2c. Find the volume of the ice cream shown below. Use 3.14 for pi. Round all answers to 1 decimal place.
Please help!!!
On solving the provided question, we can say that volume of the toy = volume of cylinder + volume of hemi-sphere Volume, V = [tex]\pi r^2 + 2/3\pi r^3[/tex] V = [tex]3.14*2*2*3 + 2/3*3.14*2*2*2[/tex] = 54.4266666667 = 54 cubic in.
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
volume of the toy = volume of cylinder + volume of hemi-sphere
Volume, V = [tex]\pi r^2 + 2/3\pi r^3[/tex]
V = [tex]3.14*2*2*3 + 2/3*3.14*2*2*2[/tex] = 54.4266666667 = 54 cubic in.
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Becca needs to find the volume of the following composite figure formed by stacking a triangular prism on top of a cube.She finds the volume of the cube by multiplying 10 by 10 by 10 to get 1,000 cubic cm. Then, she multiples by 1.5 to get the total volume of the figure. Is Becca's solution correct? Why or why not?
Becca's solution is not correct. Multiplying the volume of the cube (10 x 10 x 10 = 1,000 cubic cm) by 1.5 will not give the correct total volume of the composite figure.
Is this solution of Bella correct?From the information, Becca needs to find the volume of the following composite figure formed by stacking a triangular prism on top of a cube.She finds the volume of the cube by multiplying 10 by 10 by 10 to get 1,000 cubic cm. Then, she multiples by 1.5 to get the total volume of the figure.
The solution is incorrect is because the triangular prism and the cube are separate shapes and their volumes need to be added together to find the total volume of the composite figure. Becca needs to calculate the volume of the triangular prism separately and add it to the volume of the cube to find the total volume of the composite figure.
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Will give brainliest !! Just pls help: the mean of 10, 15, and 23 is the same as the mean of 18, 20 and ____ What number goes in the box?
Answer: 23
Step-by-step explanation:
Answer:23
Step-by-step explanation:
Use a line of fit through (9, 80) and (15, 50) to find the equation of the line in slope-intercept form.
what is the difference between 880 and 580
Solve r-4<-6.
The solution of the inequality is
Graph the solution.
When the inequality is solved, we have r-2. Each side can be multiplied or divided by the identical positive value, added to or subtracted from by the same amount, and more.
Why is there an inequality in a linear equation?Using inequality characters like "," ">," "," or "," expressions using linear inequalities compare exactly two values. Such values could be algebraic, numerical, or both.
Here,
Linear inequalities: How are they solved
In the first step, solve the equality for y.
Step 2: Sketch the boundaries of the inequality on a graph.
The region that addresses the inequality should be shaded. Step 3. Step four requires you to solve the third inequality for y. In step 5, the boundary line of the second inequality must be graphed. Cover the region that fulfills the second condition.
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