Given a random sample of 269 students and a contigency table that gives the 2 way classification of their responses.
The probability formula is:
[tex]P(E)=\frac{n(\text{Required outcome)}}{n(\text{Possible outcome)}}[/tex][tex]P(\text{Female)}=\frac{(99+22)}{269}=\frac{121}{269}=0.450[/tex][tex]P(\text{Car)}=\frac{(87+99)}{269}=\frac{186}{269}=0.691[/tex][tex]\begin{gathered} P(\text{Female}|\text{Truck)}=\frac{P(\text{Female }\cap\text{ Truck)}}{P(\text{Truck)}} \\ =\frac{22}{(61+22)}=\frac{22}{83}=0.265 \end{gathered}[/tex][tex]P(\text{Truck }\cap\text{ Female)=}\frac{22}{(99+22)}=\frac{22}{121}=0.182[/tex]The conditional probability P(A/B) or P(B/A) arises only in the case of dependent events.
An inverse variation includes the points (10, 2) and (n, 4). Find n.
SOLUTION
An inverse variation is given as
[tex]\begin{gathered} a\text{ }\propto\text{ }\frac{1}{b} \\ \text{Introducing a constant k, we have } \\ a\text{ = }\frac{k}{b} \end{gathered}[/tex]Putting a = 10 and b = 2, we have;
[tex]\begin{gathered} 10\text{ = }\frac{k}{2} \\ k\text{ = 10 x 2 = 20 } \end{gathered}[/tex]The relationship becomes
[tex]\begin{gathered} a\text{ = }\frac{20}{b} \\ \text{Putting a = n, and b = 4, we have } \\ n\text{ = }\frac{20}{4} \\ \\ n\text{ = 5} \end{gathered}[/tex]Therefore, n = 5
Trevor's bonus last year with $6720 and this was 12% of his base salary. what is his base salary?
Answer:
$56,000.
Explanation:
Let his base salary = s
12% of his base salary = $6720
Thus, we have:
[tex]12\%\text{ of s=6720}[/tex]Next, solve for s:
[tex]\begin{gathered} \frac{12}{100}\times s=6720 \\ 12s=6720\times100 \\ s=\frac{6720\times100}{12} \\ s=56,000 \end{gathered}[/tex]His base salary is $56,000.
One weekend, 5,780 people saw a new movie at 17 different theaters. Each theater sold tickets at $7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?
The amount that each theater make if they received the same number of moviegoers will be $2550.
How to calculate the amount?From the information, 5,780 people saw a new movie at 17 different theaters and each theater sold tickets at $7.50 a piece.
Therefore, the amount that each theater make if they received the same number of moviegoers will be:
= (5780 × $7.50) / 17
= $43350 / 17
= $2550
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A machine used to paint white lines on a road uses 250 litres of paint for
each 8km of road marked. Calculate:
a how many litres of paint would be needed for 200km of road
b what length of road could be marked with 4000 litres of paint.
a) Amount of paint needed for 200 km road = 6250 litres
b) Length of road that can be painted by using 4000 litres of paint = 128 km
Amount of paint used for painting white lines on road= 250 litres
Length which was painted = 8 km
By using unitary method;
Thus for 1 km amount of paint required = 250/8
= 31.25 litres
a) Amount of paint needed for 200 km road = 31.25 × 200
= 6250 litres.
therefore, Amount of paint needed for 200 km road = 6250 litres
b) Since for 1 km 31.25 liters paint is required this implies with 1 liter = 1/ 31.25 = 0.032 km can be covered.
Length of road that can be painted by using 4000 litres of paint = 4000× 0.032
= 128 km
Thus, Length of road that can be painted by using 4000 litres of paint = 128 km
What is unitary method?A single or unique unit is referred to as unitary. Determining values in relation to a single unit is the goal of this strategy. For instance, we can use the unitary technique to determine how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
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Determine if the function below is continuous.A. not continuous, >2 holesOB. not continuous, 1 holeOC. not continuous, 2 holesOD. continuousReset Selection
Given:
A graph
To determine if the given function is continuous, we first note that the given function has gaps or holes. As we can see, the function has two holes.
We must also remember that a function that has any hole or break in its graph is known as a discontinuous function.
Therefore, the answer is:
[tex]C.\text{ not continuous, 2 holes}[/tex]
"I just made a purchase of $130.00 but, once I got to my car and looked at the receipt, I realized that the salesperson who helped me did not apply the 15% discount."
Employee: "I sincerely apologize for our oversight. I will refund __________ back to your credit card."
Answer:
19.5
all you had to do was divide 15% with 130.00
A= hlba)10. The volume of a large can of tuna fish can be calculated using the formula V = ar?h.Write an equation to find the radius, r, in terms of V and h. Determine the diameter, tothe nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and aheight of 3.3 inches.
Given the formula for volume:
[tex]V\text{ = }\pi r^2h[/tex]Let's rewrite the formula in terms r, V and h.
i) Rewriting for r in terms of V and h :
[tex]\begin{gathered} V\text{ = }\pi r^2h \\ \frac{V}{h}=\pi r^2 \\ \\ \sqrt[]{\frac{V}{\pi h}}=r \\ \\ r\text{ = }\sqrt[]{\frac{V}{\pi h}} \end{gathered}[/tex]2) Given:
Volume, V = 66 cubic inches
height, h = 3.3 inches
We know that diameter is radius multiplied by 2.
To find the diameter, first find the radius.
Therefore, we have:
[tex]\begin{gathered} r\text{ = }\sqrt[]{\frac{V}{\pi h}} \\ \\ r\text{ = }\sqrt[]{\frac{66}{3.3\pi}} \\ \\ r\text{ = }2.52\text{ inches} \end{gathered}[/tex]Since the radius is 2.52 inches, the dia,eter will be:
D = r x 2 = 2.52 x 2 = 5.04 inches
To the nearest inch = 5 inches
ANSWER:
diameter = 5 inches
Write the equation for the graph below.Tomato Prices108Price (In dollars)01 2 3 4 5 6 7 8 9 10Weight(in pounds)
The form of the linear equation is
y = m x + b
m is the slope of the line
b is the y-intercept
The rule of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex](x1, y1) and (x2, y2) are two points on the line
Since (0,0) and (10, 12) are two points on the line
x1 = 0 and y1 = 0
x2 = 10 and y2 = 12
Now substitute them in the rule to find m
[tex]m=\frac{12-0}{10-0}=\frac{12}{10}=1.2[/tex]The slope of the line is 1.2
Substitute it in the form of the equation
y = 1.2 x + b
b is the y-intercept which means value y at x = 0
Since at x = 0, y = 0
Then b = 0
The equation of the line is
y = 1.2 x
Four years after paying $2700 for shares in a startup company, you sell the shares for $1300 (at a loss).
Based on the amount you paid for the shares and the selling price as well as the number of years, the total return would be -51.9%
The annual return would be -16.7%
How to find the total return?The total return on the stock can be found by finding the difference in stock prices for the 4 years and dividing by the buying price:
= (1,300 - 2,700) / 2,700 x 100%
= -1,400 / 2,700 x 100%
= 0.51851851851851851851851851851852 x 100%
= -51.9%
The annual return can be found as:
= ((1,300 / 2,700) ^ 1/4 - 1) x 100%
= -16.7%
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Together, Nora and Addison own 152 shares of stock. Nora has 4 less than three times Addison's amount. How many shares does each girl have?
Dora have 144 shares of stocks while Addison have 37 shares of stocks.
Let us say that Addison own X shares of stock.
According to the situation provided,
The number of shares of stocks own by Dora are 4 less than 3 times of the Stocks owned by Addison.
Stocks Owned by Dora = 3x - 4
The total shares of stocks are 152.
So, we can write the relation between the stocks as,
x + 3x - 4 = 152
4x - 4 = 152
The above formed relations between the stocks is in the form of linear equation in one variable. A linear equation has highest power of variable equal to 1 and only one variable.
Now, solving the equation further,
4x - 4 = 152
4x = 148
x = 37
The total numbers of stocks owned by Addison are 37.
Shares of stocks owned by Dora are 3(37)-4.
The share of stocks owned by Dora are 144.
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3. Solve the absolute inequality |2x + 3| < x + 6
Answer
The solution is
-3 < x < 3
Explanation
To solve an expression with the absolute value symbol. we obtain two solutions for it.
We first solve when the other side of the equation to the absolute value symbol has positive sign.
Then, we obtain another solution by setting that other side (the right-hand side) to negative. For equations involving inequality signs, the second solution usually changes the inequality sign.
| 2x + 3 | < x + 6
First solution
2x + 3 < x + 6
2x - x < 6 - 3
x < 3
Second solution
2x + 3 > -(x + 6)
2x + 3 > -x - 6
2x + x > -6 - 3
3x > -9
Divide both sides by 3
(3x/3) > (-9/3)
x > -3
So, the solution written together,
x > -3 and x < 3
together, it is
-3 < x < 3
Hope this Helps!!!
What's the missing side
the answer choices area. y = 1/3x +2b. y = 2x + 1/3c. y = -1/3x. + 2d. y = -2x - 1/3
We have to find the line equation of the function shown. We see that passes through the points:
[tex](0,2)\text{ and }(3,1)[/tex]For doing so, we will find the slope and the y-intercept. The slope is given by the expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x₁,y₁) and (x₂,y₂) are two points of the line. In this case, replacing we obtain:
[tex]m=\frac{1-2}{3-0}=\frac{-1}{3}=-\frac{1}{3}[/tex]And thus, the slope is - 1/3. Now, for the y-intercept, we remember that when the x-coordinate is 0, the y-intercept is the y-coordinate.
As the line passes through the point (0,2), the y-intercept will be 2.
Putting those two together, the equation of the line will be:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]How do you do this step by step?
-7 + 9 + (-8)
Step-by-step explanation:
-7 + 9 + (-8)
2 + (-8)
-6
Hope this helps! :)
Step-by-step explanation: Remove parenthesis. If there is a "+" in front of an expression in parenthesis, the expression remains the same.
-7+9-8. Calculate the sum or difference. You should get -6.
a square flowerbed has an area of 12 sq feet.find length of pne side of the square in ft/in rounded to the nearest in.
Area of square = L x L
12sq feet =L x L
[tex]\begin{gathered} L=\sqrt[]{12} \\ L=3.46\approx3\text{ f}eet \end{gathered}[/tex]How many ways can you arrange 4 books on a shelf?
In order to find the number of ways, we must simply calculate:
4! = 4*3*2*1 = 24
24 possible ways.
Ms.Macncheese has 7 plates of fish sticks if she ate 4 how many dose she have left?
A. 3
B. 2
C.1
D.11
Answer:
3
Step-by-step explanation:
7 - 4 is 3
write down in terms of n, an expression for the nth term of the following sequences
-7,-12,-17,-22,-27
The expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
The sequence is -7, -12, -17, -22, -27...
The first term = -7
The common difference = The second term - The first term
= -12 - (-7)
= -12+7
= -5
The nth term of the sequence = a+(n-1)d
Where a is the first term
d is the common difference
n is the n terms
Substitute the values in the equation
The nth term of the sequence = -7+(n-1)-5
= -7-5n+5
= -5n-2
Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
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The country of Latveria has a population of 11.2 million at the start of 1988, which grows at 4.4% per year.A) Write a recursive equation for the population of Latveria.B) Write an explicit equation for the population of Latveria.C) To the nearest tenth of a million, what is the population of Latveria at the start of 1994.
A) The recursive formula takes into account the previous term. For each term, the next term is expressed in respect to it
Looking at the given scenario, the popularion is increasing by 4.4%. This means that the common ratio is
1 + 4.4/100 = 1.044
Given that the initial population is 11200000, the recaursive formula or equation would be
[tex]\begin{gathered} f_n=\text{ 1.044}f_{n\text{ - 1}} \\ \text{where f}_1=\text{ 11200000} \end{gathered}[/tex]B) For the explicit formula, the general formula for a geometric sequence is
an = a1 * r^(n - 1)
a1 = first term = 11200000
r = common ratio = 1.044
The explicit equation would be
an = 11200000 * 1.044^(n - 1)
C) At the start of 1994, the number of terms, n = 7
We would find a7 by substituting n = 7 into the explicit equation. We have
a7 = 11200000 * 1.044^(7 - 1)
a7 = 11200000 * 1.044^6 = 14501770
At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
The cost of the 5 bags using proportionality method is: $36.25
What is proportionality?
In mathematics, the term proportionality can be defined by considering a two quantities in constant ratio. And the two quantities can be recognized as the variable y and x. Where, the variable y is defined as directly proportionate to the changes in the variable x which is based on its constant ratio.
According to the question, the given data states that 5 bags will cost $36.25.
By using proportionality method to solve the given statement. Put the price over the number of bags
21.75 x
---------- = ---------
3 bags 5 bags
Using cross products defined in standard mathematics,
21.75 * 5 = 3x
108.75 = 3x
Divide each side by 3
108.75/3 = 3x/3
36.25 =x
5 bags will cost 36.25
Hence, the cost of the 5 bags using proportionality method is: $36.25
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Correct Question:
At the nearest wholesale store, 3 bags of bulk cereal cost $21.75. At this rate, how much would 5 bags of bulk cereal cost?
Delta Simply Fraction Exponent
solve the equations and verify the answer
Answer:
See below
Step-by-step explanation:
I THINK what you wrote is:
2(x-2) - 3(x-3) = (5x-5) - 4(x-8)
2x -4 -3x+9 = 5x-5 -4x+ 32
2x-3x-5x+4x = 4 -9 -5 +32
-2x = 22 *** EDITED ***
x = - 11
How much hectares is 61,230 km²
Answer:
6 hecters in the khlathmandu
How much grain can a farmer hold in this silo? Use π = 3.14.A. 2,093.3 ft³B. 11,513.3 ft³C. 9,420 ft³D. 12,560.2 ft³
To find out how much grain the farmer can hold we need to find the volume of the silo. The silo is made from a circular cylinder and half a sphere.
The volume of the cylinder is given by:
[tex]V=\pi r^2h[/tex]In this case r=10 and h=30, plugging this values in the equation above we have that the volume of the cylinder is:
[tex]\begin{gathered} V=(3.14)(10)^2(30) \\ V=9420 \end{gathered}[/tex]Hence the volume of the cylinder is 9420 cubic feet.
Now we need to find the volume ot half the sphere, the volume og an sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Plugging the radius we have that:
[tex]\begin{gathered} V=\frac{4}{3}(3.14)(10)^3 \\ V=4186.6 \end{gathered}[/tex]Now, we only need half this volume then the volume of the top of the silo is:
[tex]V=2093.3[/tex]Finally we add the volume of the cylinder and half the sphere, therefore the volume of the sylo is:
[tex]11513.3[/tex]and the answer is B.
the function shown is in the form y= ( x - h)² Determine the value of h.A) -1 B) 1C) 2D) -1/2
INFORMATION:
We have the graph of a function that has the form y = ( x - h)² and we must find the value of h.
STEP BY STEP EXPLANATION:
we can see that the graph is a parabola which its vertex is at the point (2, 0)
Now, having this point we can replace the values of its components in the formula of the function
Since the point is (2, 0), then x = 2 and y = 0
[tex]0=(2-h)^2[/tex]Finally, we must solve the equation for h
[tex]\begin{gathered} 0=(2-h)^{2} \\ \sqrt[]{0}=2-h \\ 0-2=-h \\ 2=h \\ h=2 \end{gathered}[/tex]ANSWER:
C) 2
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
Slope: 0
Ordered Pair: (-9,7)
The equation of the line woth slope 0 and passing through (-9,7) in slope-intercept form is y = 7.
If a line L has a slope M and it has the intercept c, then the equation of the line L can be written in the point slope form as,
L : y = Mx + c
This above equation of line is known as slope-intercept form of line.
Here, we have to find the equation of line which has slope m equal to zero and passing through (-9,7).
putting the known values in y = mx+c
y = (0)x+ c
y = c
Putting the value of y = 7
c = 7
Here, we have,
y = 7
So, the equation of the required line is y=7.
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i want to plant 45 sunflower plants and 63 tomato plants in my garden. if i put the same number of plants in each row with only one type of plant in each row, what is the greatest number of plants i can put in one row? Show evidence
9 is the greatest number of plants in one row.
What is HCF?The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.
To find the greatest number of plants she can put in one row , need to find
HCF of 45 , 81 and 63
45 = 3× 3 × 5 = 3² ×5¹
63 = 3 ×3 × 7 = 3² × 7¹
HCF Highest common factor of given numbers is the largest factors which divides all the given numbers perfectly.
HCF = product of common factors of least power
HCF = 3² = 9
Hence greatest number of plants she can put in one row is 9
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What number can be divided into 9 equal groups without a remainder?
A. 256
B. 387
C. 424
D. 532
Answer:
B
Step-by-step explanation:
387/9 = 43
1. In 2003, the U.S. imported one million, eight hundred seventy thousand 2 barrels of crude oil per day. In 1988. the U.S, imported only nine hundred eleven thousand barrels per day. How many fewer barrels per day did the U.S. import in 1988? Write the equation.
Let's begin by identifying key information given to us:
Import (2008) = 1,870,000 bbl
Import (2008) =
The variables x and y vary directly. Write an equation that relates the variable. Then find x when y=16.
7) We know that x = 5 and y = 2
We can write an equation that relates this values as a proportion.
Let's say there is a number r such as:
x*r=y
That's a equation that relates x and y. Let's solve for the values given.
[tex]5\cdot r=2[/tex]Now solve for r:
[tex]r=\frac{2}{5}[/tex]The relation we found is:
[tex]x\cdot\frac{2}{5}=y[/tex]Now to find the value of x when y = -6, we replace it in the equation:
[tex]\begin{gathered} x\cdot\frac{2}{5}=-6 \\ x=-6\cdot\frac{5}{2}=-15 \end{gathered}[/tex]Then with this relation, x = -15 when y = -6