Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Related Questions
8. What is the solution to the following equation? (1 point)
x² - 10x + 24 = 0
Ox= 3 or x = 8
Ox= -3 or x = -8
Ox=4 or x =
Ox=-4 or x = -6
9. Ms. Ortiz sells tomatoes wholesale. The function p(x) = -80x² + 320x
Answers
The solution of the equation x² - 10x + 24 = 0 is x = 4 or x = 6. Option C is correct.
We are given a quadratic equation:
x² - 10x + 24 = 0
Let us split the middle term, we will get;
x² - 6x - 4x + 24 = 0
x (x - 6) - 4 (x - 6) = 0
(x - 4) (x - 6) = 0
equate each with zero, we will get;
x - 4 = 0 or x - 6 = 0
x = 4 or x = 6
So, the value of x is 4 or 6.
So, option C full fills the required criteria.
Thus, the solution of the equation x² - 10x + 24 = 0 is x = 4 or x = 6. Option C is correct.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
2(3+x)=18 what does x equal
Answers
We need to solve the following equation:
[tex]\begin{gathered} 2(3+x)=18 \\ \end{gathered}[/tex]In order to do that, we have to isolate the "x" variable on the left side.
[tex]\begin{gathered} 2\cdot3+2\cdot x=18 \\ 6+2\cdot x=18 \\ 2\cdot x=18-6 \\ 2\cdot x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]The value of x is 6.
Look at the steps for constructing a perpendicular bisector of a line segment.
Which is an accurate description for step 2?
Draw arcs, using a compass, above and below line segment XY with X as the center with a width of less than half of line segment XY.
Draw arcs, using a compass, above and below line segment XY with X as the center with a width of more than half of line segment XY.
Draw arcs, using a compass, above line segment XY with X as the center and below line segment XY with Y as the center with a width of more than half of line segment XY
Draw arcs, using a compass, above line segment XY with X as the center and below line segment XY with Y as the center with a width equal to the half of the segment XY
Answers
The accurate description for step 2 is "Draw arcs, using a compass, above and below line segment XY with X as the center with a width of more than half of line segment XY."
What is Perpendicular Bisector?
A line that divides a line segment into two equal halves and forms a 90-degree angle at the point of intersection is called a perpendicular bisector. The word "bisect" refers to dividing equally.
By looking at the steps for constructing a perpendicular bisector of a line segment.
The accurate description for step 2 is below.
That is "Draw arcs, using a compass, above and below line segment XY with X as the center with a width of more than half of line segment XY."
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Help please!!!
It’s about ratios
Answers
Answer:
B
Step-by-step explanation:
Proportional means that the values should be equal to each other:
15/21= 0.714...
20/25= 0.8
20/24=0.833...
15/18= 0.833...
16/20=0.8
20/24=0.8333...
5/6=0.8333...
6/5=1.2
Hope this helps!
please HELP!!! GUYS
the homework is due tom
Answers
Answer:
A(-4.5;2) B(0;-3.5).......
a food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. if the sample mean is 15.2 oz and the sample standard deviation is 0.70 oz, find the 95% confidence interval of the true mean.
Answers
95% confidence interval is (14.55, 15.85)
From the question, we have
Degrees of freedom = n - 1 = 7 - 1 = 6
For 6 degrees of freedom and 95% confidence interval:
Critical t value = 2.45
95% confidence interval is:
15.2 \pm 2.45*0.70/\sqrt{7}
15.2 \pm 0.65
(14.55, 15.85)
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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given the function y=3x + 5 find the range uf the domain is (-4,-1,2,5,)
Answers
The function we have is:
[tex]y=3x+5[/tex]We are given the domain of the function:
[tex]D=(-4,-1,2,5)[/tex]The domain of a function is the allowed values for x.
And we are asked to find the range, which is the values that the function returns for the x-values of the domain.
To find the range, we need to take the values of the domain, substitute them into the equation, and find the values that the function returns.
For the given domain, the allowed values for x are:
[tex]\begin{gathered} x=-4 \\ x=-1 \\ x=2 \\ x=5 \end{gathered}[/tex]For x=-4
We substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(-4)+5 \end{gathered}[/tex]And solve to find the first value of the range:
[tex]\begin{gathered} y=-12+5 \\ y=-7 \end{gathered}[/tex]For x=-1
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(-1)+5 \end{gathered}[/tex]Solve the operations:
[tex]\begin{gathered} y=-3+5 \\ y=2 \end{gathered}[/tex]For x=2
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(2)+5 \end{gathered}[/tex]And again, solve the operations:
[tex]\begin{gathered} y=6+5 \\ y=11 \end{gathered}[/tex]For x=5
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(5)+5 \end{gathered}[/tex]Solve the operations:
[tex]\begin{gathered} y=15+5 \\ y=20 \end{gathered}[/tex]The values we have found for y are the range of the function:
[tex]R=(-7,2,11,20)[/tex]Answer:
The range of the function is (-7,2,11,20)
What is the value of x in the equation 25x^2 = 16?O A ±5/4OB. ±4OC. ±4/5OD. ±16/25
Answers
Answer:
C. ±4/5
Explanation:
Given the equation
[tex]25x^2=16[/tex]The first step is to divide both sides by 25 to isolate the variable x.
[tex]\begin{gathered} \frac{25x^2}{25}=\frac{16}{25} \\ x^2=\frac{16}{25} \end{gathered}[/tex]Next, we take the square roots of both sides of the equation.
[tex]\begin{gathered} \sqrt{x^2}=\pm\sqrt{\frac{16}{25}} \\ x=\pm\frac{4}{5} \end{gathered}[/tex]The correct choice is C.
Equation of a line two-points form
The line passes through (1, -2) and (-2, -2)
Answers
Answer:
y = - 2
Step-by-step explanation:
the equation of a line passing through points with the same y- coordinates is
y = c ( where c is the value of the y- coordinate )
the line passes through (1, - 2 ) and (- 2, - 2 ) both with y- coordinate - 2, so
y = - 2 ← equation of line
The area of a quadrant of a circle is 8 cm². Find the radius and perimeter.
Answers
The radius of the circle will be 3.19.
The perimeter of the circle will be 20.03.
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The area of a quadrant of a circle is 8 cm².
Now,
Since, We know that;
The area of a quadrant of a circle = πr² / 4
So, We can formulate;
⇒ πr² / 4 = 8
Solve for r as;
⇒ 3.14 x r² = 8 x 4
⇒ r² = 32/3.14
⇒ r² = 10.19
⇒ r = √10.19
⇒ r = 3.19
Since, The perimeter of the circle = 2πr
Substitute all the values, we get;
The perimeter of the circle = 2πr
The perimeter of the circle = 2 x 3.14 x 3.19
= 20.03
Thus, The radius of the circle will be 3.19.
The perimeter of the circle will be 20.03.
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Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.8. 3, 9, 15, 21, 27,9. 5, 9, 13, 17, 21,10. -243, 81, -27, 9,11. Using the sequence find the n for the following terms 6, 1, 4,-9...... -254
Answers
see explanation below
Explanation:8) 3, 9, 15, 21, 27
The common difference = 15-9 = 9-3
The common difference = d = 6
Hence, it is an arithmetric sequence
The recursive formula:
[tex]\begin{gathered} a_{n+1}=a_n+\text{ 6} \\ \text{OR} \\ a_n=a_{n-1}+\text{ d} \\ a_n=a_{n-1}+6 \end{gathered}[/tex]The appropriate formula:
[tex]\begin{gathered} a_n=a_1+\text{ (n-1)d} \\ \text{where a}_1\text{ = }3\text{ } \\ a_n=3_{}+\text{ (n-1)d} \end{gathered}[/tex]The next three numbers in the sequence:
[tex]\begin{gathered} \text{The last term in the sequence given was 6th term. } \\ \text{The next }3\text{ terms will be: 7th, 8th and 9th term} \end{gathered}[/tex][tex]\begin{gathered} a_7\text{ = 3 + (7-1)}\times6 \\ =\text{ 3+ (6)(6) = 3 + 36} \\ 7th\text{ term = }a_7=39 \end{gathered}[/tex][tex]\begin{gathered} a_8\text{ = 3 + (8-1)}\times6 \\ =\text{ 3+ (7)(6) = 3 + 4}2 \\ 8th\text{ term = }a_8\text{ =}45 \end{gathered}[/tex][tex]\begin{gathered} a_9\text{ = 3 + (9-1)}\times6 \\ a_9\text{ = }3\text{ + 8(6) = 3 + 48} \\ 9th\text{ term = }51 \\ \end{gathered}[/tex]SOMEONE HELP ME WITH THIS
Answers
Answer:
A = 44
Step-by-step explanation:
11 x 8 = 88
88 / 2 = 44
1) When we solve systems of linear equations, we are finding the valuesfor x and y that are true for both equations in a system. What does thissolution indicate on a graph?
Answers
Answer
The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.
The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection.
Explanation
The graph of a system of equations show straight lines that correspond to each of the equations.
The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.
The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection.
Hope this Helps!!!
Answer:
The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines.
The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection
Step-by-step explanation
The graph of a system of equations show straight lines that correspond to each of the equations. The solution of this system of equations is usually the point where the lines meet each other. The solution is at the point of intersection of the lines. The value for x is the x-coordinate of this point of intersection and the value for y is the y-coordinate of this point of intersection
What is the height, x, of the equilateral triangle shown?
an equilateral triangle with the angles labeled as 60 degrees and a side length of 10 inches, the height labeled as x
Answers
The equilateral triangle's height, (x), is 7√3 inches.
What are Equilateral triangles?An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.So, the equilateral triangle's side length is 14 inches.
As a result, we may use the Pythagoras theorem to determine the triangle's height.
c² = a² + b²Now, substitute the values and calculate as follows:'
c² = a² + b²14² - 7² = b²b² = 196 - 49b² = 147b = 7√3Therefore, the equilateral triangle's height, (x), is 7√3 inches.
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Complete question:
What is the height, x, of the equilateral triangle?
An equilateral triangle with angles labeled as 60 degrees and a side length of 14 inches, the height labeled as x
the sum of 3 and twice a number is 33
Answers
hello
to solve this question, we should let the unknown number be represented by x
[tex]\begin{gathered} x+2x=33 \\ 3x=33 \\ \text{divide both sides by the coefficient of x} \\ \frac{3x}{3}=\frac{33}{3} \\ x=11 \end{gathered}[/tex]the first number (x) is equal to 11, we can find the other number.
[tex]2x=2\times11=22[/tex]from the calculations above, the numbers are 11 and 22
8th grade mathWhich quadrant is the answer to this system of equations in?A. Quadrant 1B. Quadrant 2 C. Quadrant 3D. Quadrant 4
Answers
Given the figure, we can deduce the following information:
1. The lines intersect at point (-2,-2).
To determine which quadrant is the answer to the given system of equations, we note the quadrants as shown below:
Based on the given graph, we can notice that the lines intersect at point (-2,-2) which is located at Quadrant 3.
Therefore, the answer is C. Quadrant 3.
Which of these is the absolute value parent function?O A. f(x) = 5x - 11B. f(x) = 13x1c. f(x) = \x{ + 2OD. f(x) = |x|
Answers
Concept
The parent function of absolute functions is y = |x|, and it passes through the origin.
So a parent absolute function is a function that have not been transformed.
So the absolute value parent function is f(x) = |x|
Final answer
f(x) = |x|
The product of 14 and x is equal to 28 more than x.
Answers
The value of x is given by 28/13.
Given the product of 14 and x is = 14*x = 14x
According to question, the product is equal to 28 more than x. So,
14x = 28+x
14x-x = 28
13x = 28
x = 28/13
Hence the value of x is 28/13.
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A small business sells sno-cones at the southern end of the amusement park. They had to pay the amusement park $8,500 for the space to sell the sno-cones, and it costs the business $0.80 in supplies for each sno-cone they sell.
If the small business can afford to pay less than $30,000 in expenses for the summer, what is the maximum number of sno-cones they can afford to sell?
Answers
Answer:
Step-by-step explanation:
In the summer time your friend wants to have a snow cone stand at a local grocery store parking lot. You want to make sure he actually makes money. The grocery store charges $300 per month. All products are calculated to be 25 cents per customer. Your plans are to sell each cone for $1.25. a. Write a mathematical expression representing the cost of operation for a month. b. Write a mathematical expression representing sales. c. Create an equation that will represent overall profit of the operation for a month. d. Simplify the equation into slope intercept form and standard form. What is the slope and explain its meaning in the context of selling snow cones? What is the intercept and what is its meaning? e. Describe the method of graphing the slope intercept form and also the standard form of the equation. f. What is the domain and range of the equation? Is the relation a function, why? g. How many snow cones do you need to sell to break even in the first month? h. How much is the profit if you sell 425, 550 or 700 snow cones in the first month of business? . Thomas and Jenny went to a bakery to pick up some cookies for dessert. Thomas bought 3 pumpkin cookies and 2 raisin cookies. Jenny bought 2 pumpkin cookies and 4 raisin cookies. Thomas consumed 870 calories and Jenny consumed 750 calories. a. Write a system of equations to represent this situation. b. Solve each equation for y and graph to find the solution. How many calories are the pumpkin and raisin cookies? c. Solve the same equations using substitution and the elimination methods. Compare all of your answers. Perform the following to demonstrate you can work with geometric sequences: a. Write 5 numbers that are an example of a geometric sequence. b. Show the value of the common ratio. c. Write an equation that would give you the value of the 23rd term in the sequence d. Find the sum of the first 10 terms of the sequence. Show your work or explain you answer.
A dentist kept a record of the number of new cavities his patients had per year for the last 10 years. The scatterplot below shows the average number of new cavities per year for patients in the 4-to 32-year age range. Which of the following best describes the trend line of the data shown in the scatterplot? O a horizontal line a line with a negative slope, a line with a positive slope,no trend line
Answers
Line r has an equation of y + 3 = -(x + 2). Line s includes the point (-10, -8) and is
parallel to line r. What is the equation of line s?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answers
Answer:
y = - x - 18
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
the equation of a line in point- slope form is
y - b = m (x - a)
m is the slope and (a, b ) a point on the line
y + 3 = - (x + 2) ← is in point- slope form
with slope m = - 1
• Parallel lines have equal slopes , then
y = - x + c ← is the partial equation
to find c substitute (- 10, - 8 ) into the partial equation
- 8 = 10 + c ⇒ c = - 8 - 10 = - 18
y = - x - 18 ← equation of line s
The equation in slope-intercept form is y=-x-18.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, Line r has an equation of y + 3 = -(x + 2).
y+3=-x+2
y=-x+2-3
y=-x-1
Here, slope m=-1
Line s includes the point (-10, -8) and is parallel to line r.
The slope of a line parallel to given line is m1=m2
Substitute m=-1 and (x, y)=(-10, -8) in y=mx+c, we get
-8=-1(-10)+c
c=-18
So, the equation is y=-x-18
Therefore, the equation in slope-intercept form is y=-x-18.
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2. How does scale factor change the area?
A. by the scale factor
B. by the scale factor cubed
C. by the scale factor squared
Answers
The area will change if the scale factor length is increased or reduced.
Option A is the correct answer.
What is the scale factor?
This refers to the extent to which a shape is increased or reduced. It is used in drawings of shapes eg rectangles, squares, circles, etc.
What is area?
This refers to the total space occupied by a particular shape or object. it is measured in square meters,m².
The area of an object can change, if the scale factor is increased or reduced by a particular amount.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
Choose the correct equation type for each system. ry = 3x - 2 |3x-y=4 Consistent S-y = -x +5 12y = -4x + 20 y = -x + 4 [x=-y-6 > y = 4x + 2 y = 6x - 10 (y=2x+1 y = -2x + 3 =+3 - 2x + 5y = 0 y = x
Answers
Let's solve each system to check if it is a consistent or inconsisent system of equations:
a.
[tex]\begin{gathered} \begin{cases}y=3x-2 \\ 3x-y=4\end{cases} \\ \text{ Substituting the value of y from the first equation in the second:} \\ 3x-(3x-2)=4 \\ 3x-3x+2=4 \\ 2=4 \end{gathered}[/tex]This system has no solution, therefore it is a inconsistent system.
b.
[tex]\begin{gathered} \begin{cases}\frac{1}{2}y=-x+5 \\ 2y=-4x+20\end{cases} \\ \text{Multiplying the first equation by 4:} \\ 2y=-4x+20 \end{gathered}[/tex]Both equations represent the same line, so the system has infinite solutions, therefore it is a consistent dependent system.
c.
[tex]\begin{gathered} \begin{cases}y=-x+4 \\ x=-y-6\end{cases} \\ \text{ Applying the value of y from the first equation in the second one:} \\ x=-(-x+4)-6 \\ x=x-4-6 \\ 0=-10 \end{gathered}[/tex]This system has no solution, therefore it is a inconsistent system.
d.
[tex]\begin{gathered} \begin{cases}y=4x+2 \\ y=6x-10\end{cases} \\ \text{Comparing the y values:} \\ 4x+2=6x-10 \\ 6x-4x=2+10 \\ 2x=12 \\ x=6 \\ \\ y=4\cdot6+2=24+2=26 \end{gathered}[/tex]This system has one solution, therefore it is a consistent independent system.
e.
[tex]\begin{gathered} \begin{cases}y=2x+1 \\ y=-2x+3\end{cases} \\ \text{Comparing the y values:} \\ 2x+1=-2x+3 \\ 2x+2x=3-1 \\ 4x=2 \\ x=\frac{1}{2} \\ \\ y=2\cdot\frac{1}{2}+1=1+1=2 \end{gathered}[/tex]This system has one solution, therefore it is a consistent independent system.
f.
[tex]\begin{gathered} \begin{cases}-2x+5y=0 \\ y=\frac{2}{5}x\end{cases} \\ \text{ Applying the value of y from the second equation in the first one:} \\ -2x+5\cdot(\frac{2}{5}x)=0 \\ -2x+2x=0 \\ 0=0 \end{gathered}[/tex]This system has infinite solutions (the equations represent the same line), therefore it is a consistent dependent system.
24 divided by (-3/2)
Need help please:)
Answers
I WILL GIVE LOTS OF POINTS
give me the answer for these algebra equations!
Answers
The slope intercept form of the required line is x + y = 5
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The given line is
x + y = 4
y = -x + 4
Slope of the line = [tex]-1[/tex]
Slope of the line parallel to this line = [tex]-1[/tex]
The line passes through (2, 3)
Equation of the required line
y - 3= -1(x - 2)
y - 3 = -x + 2
x + y = 3 + 2
x + y = 5
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The average weight of a brown bear is 1000 about pounds. suppose a large stuffed animal weighs 6.9 pounds. write a percent to compare the weight of the stuffed animal to the weight of the brown bear.
Answers
Answer:
Step-by-step explanation:
0.69
1000 = 100%. Using the cross method, multiply 6.9 by 100, then divide it by 1000. The answer should be 0.69%.
The following table represents the highest educational attainment of all adultresidents in a certain town. If a resident who has a master's degree is chosen atrandom, what is the probability that they are aged 40 or over? Round your answer tothe nearest thousandth.
Answers
The answer is: 0.0362
The total number of Master's degree holders = 2848 (from the question)
In order to choose people 40 and above from this Master's degree holder subset,
You choose:
People 40-49 AND People 50 and over.
Number of people 40-49 = 475
Number of people 50 and over = 699
But we also need to take into consideration, the probability of picking a person 40-49 years old OR 50 and over
total Number of people 40 - 49 are 3518
The total Number of people 50 and above are 6518
Thus, we can write the probability as:
[tex]\begin{gathered} P(\text{choosing 40-49)=}\frac{475}{3518} \\ P(\text{choosing 50 and above)=}\frac{699}{6518} \\ P(choo\sin g\text{ Master's degre}e)=\frac{2848}{19076} \\ \\ \text{Thus, for choosing 40-49 AND Master's degre}e\colon \\ P(\text{choosing 40-49 AND Master's degr}ee)=\frac{475}{3518}\times\frac{2848}{19076}=0.0202 \\ \\ \text{For choosing 50 and above AND Master's degre}e\colon \\ P(\text{choosing 50 and above AND Master's degree)=}\frac{699}{6518}\times\frac{2848}{19076}=0.016 \\ \\ \text{Thus choosing Master's degree holder, 40 or over:} \\ P(\text{choosing 40-49 AND Master's degr}ee)+ \\ P(\text{choosing 50 and above AND Master's degree)} \\ =0.0202+0.016=0.0362 \end{gathered}[/tex]The final answer is: 0.0362
Calculate the area??
Answers
Answer:
120cm²
Step-by-step explanation:
the figure is formed by a rectangle and two isosceles triangles, the measures of the rectangle are: 12cm and 5cm, the base of the triangles is 12cm and the height is (13 - 5) : 2 = 4cm
Rectangle Area = b × h
12 × 5 = 60cm²
Triangle Area = 1/2 b × h
1/2 12 × 5 = 30cm²
just sum the single Areas
60 + 30 + 30 =
120cm²