162 inches is 13.5 feet or 13 feet 6 inches, so it would not fit underneath the bridge
Answer:
The truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.
∠A and ∠B are supplementary, and ∠A and ∠C are supplementary. Which conclusion is valid? Select one: A. ∠B and ∠C are supplementary. B. ∠B and ∠C are acute. C. ∠B and ∠C are complementary. D. ∠B and ∠C are congruent.
Option D is the correct answer.
Answer:
D. ∠B and ∠C are congruent.
Step-by-step explanation:
Since, ∠A and ∠B are supplementary.
Therefore,
∠A + ∠B = 180°.....(1)
Since, ∠A and ∠C are supplementary.
Therefore,
∠A + ∠C = 180°.....(2)
From equations (1) & (2)
∠A + ∠B = ∠A + ∠C
=> ∠B = ∠C
Hence, ∠B and ∠C are congruent.
P(x)=3x² + 4x³-8+x⁴-7x Degree; Type; Leading coefficent;
Answer:
Degree: 4; Type: quartic; Leading coefficient: 1
Step-by-step explanation:
Q2 (i). A line “t” is parallel to 3y = 6x + 9. Find the slope of this line “t”. (ii) Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line “r”. plz can anyone tell me by doing the practice on the copy I will be thankful
Answer: 6 and -1/6
Step-by-step explanation:
solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.
Answer:
1) 2
2) -1/2
Step-by-step explanation:
1) 3y= 6x+9
y= 2x+3
Slope is 2
Parallel line "t" has the same slope, it will have equation:
y= 2x+b
2) y =2x+3
Perpendicular line"r" has a slope opposite-reciprocal to this, so the slope will be -1/2, the equation for line"r" is:
y= -1/2x +b
The gradient of the line is same as slope and it is -1/2 for line"r"
) Let an denote number of n-digit ternary sequences (sequences of 0,1 and 2) which have no consecutive 0’s in them. Find a recurrence relation for an. (Do not solve the recurrence. However, depending on the order of the recurrence, provide a sufficient number of initial conditions. )
Answer:
The recurrence relation for aₙ is aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8
Step-by-step explanation:
Solution
Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.
Ternary sequence is sequence with each of digits either 0, 1 or 2.
Now
Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.
Let us first find few initial values of aₙ
For n = 1
a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.
This 1-digit sequence can be either 0 or 1 or 2.
Thus,
a₁ = 3
For n =2
a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.
This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.
here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)
But one of these 9 sequence there are consecutive 0's .... (00)
So we eliminate this one sequence.
So, a₂ = 8
Now
let us find the recurrence relation
Fir n ≥ 3
aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.
For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2
Let assume the 1st digit of this n - digit ternary sequence is 1.
Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.
For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1
So,
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.
Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.
So
If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:
aₙ-1 + aₙ -1 = 2aₙ -1
For the second case: if 1st digit of this n - digit ternary sequence is 0
If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,
If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.
So there are 2 choices for 2nd digit.
After this there are more n-2 digits.
Then
For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them
For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.
Now,
The total number of sequence in this case is given as:
2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)
Hence
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3
Now,
The recurrence relation for aₙ is shown below:
aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3
With the initial conditions as a₁ =3; a₂ = 8
hey guys, can you help me please
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Work Shown:
The green triangle in the back has height 2.6 and an unknown base x. Half of this is x/2, which I'll call y. So y = x/2.
The green triangle in the back is split along the vertical dotted line to get two right triangles. The base of each right triangle is y = x/2.
Use the Pythagorean theorem to find y. Use that to find x
a^2+b^2 = c^2
y^2+(2.6)^2 = (3.2)^2
y^2 + 6.76 = 10.24
y^2 = 10.24 - 6.76
y^2 = 3.48
y = sqrt(3.48) .... apply square root
y = 1.8654758 approximately
x/2 = 1.8654758
x = 2*1.8654758
x = 3.7309516 also approximate
The base of the triangle is roughly 3.7309516 meters
We can now find the area of one green triangle
area of triangle = base*height/2 = 3.7309516*2.6/2 = 4.85023708
two triangles have approximate area 2*(4.85023708) = 9.70047416
----------------------------------
So far we've only considered the triangular faces. There are 3 more faces which are the rectangular sides. These are known as the lateral sides.
One way to get the lateral surface area is to multiply the perimeter of the triangle by the depth of the prism
perimeter of triangle = (side1)+(side2)+(side3)
perimeter = 3.7309516 + 3.2 + 3.2
perimeter = 10.1309516
lateral surface area = (depth)*(perimeter)
lateral surface area = (8.26)*(10.1309516)
lateral surface area = 83.681660216
----------------------------------
The last step is to add this lateral surface area onto the area of the two triangles to get the full surface area
surface area = (triangular area) + (lateral surface area)
surface area = (9.70047416) + (83.681660216)
surface area = 93.382134376
surface area = 93.382 square cm
Let U be the 3 2 matrix [0.45 0.42, 0.25 0.35, 0.15 0.15]. The first column of U lists the costs per dollar of output for manufacturing product B, and the second column lists the costs per dollar of output for manufacturing product C. The first row is the cost of materials, the second row is the cost of labor, and the third row is the cost of overhead. Let q1 be a vector in set of real numbers R2 that lists the output (measured in dollars) of products B and C manufactured during the first quarter of the year, and let q2, q3 , and q4 be the analogous vectors that list the amounts of products B and C manufactured in the second, third, and fourth quarters, respectively. Give an economic desciption of the data in the matrix UQ, where Upper Q = [q1 q2 q3 q4].A. The 4 columns of UQ list the profit made from selling products B and C during the 4 quarters of the year. B. The 3 rows of UQ list the costs for materials, labor, and overhead used to manufacture products B and C for the year. C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year. D. The 4 columns of UQ list the total number of each product manufactured during the 4 quarters of the year.
Answer:
C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year.
Step-by-step explanation:
[tex]U=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)[/tex]
[tex]q_1[/tex] is a vector in the set of real numbers [tex]R^2[/tex] that lists the output (measured in dollars) of products B and C manufactured during the first quarter of the year.
Therefore:
[tex]UQ=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)\left(\begin{array}{ccc}q_{1B}\\q_{1C}\end{array}\right)\left(\begin{array}{ccc}q_{2B}\\q_{2C}\end{array}\right)\left(\begin{array}{ccc}q_{3B}\\q_{3C}\end{array}\right)\left(\begin{array}{ccc}q_{4B}\\q_{4C}\end{array}\right)[/tex]
[tex]=\left(\begin{array}{c|c|c|c}q_1&q_2&q_3&q_4\\0.45q_{1B}+0.42q_{1C}&0.45q_{2B}+0.42q_{2C}&0.45q_{3B}+0.42q_{3C}&0.45q_{4B}+0.42q_{4C}\\0.25q_{1B}+0.35q_{1C}&0.25q_{2B}+0.35q_{2C}&0.25q_{3B}+0.35q_{3C}&0.25q_{4B}+0.35q_{4C}\\0.15q_{1B}+0.15q_{1C}&0.15q_{2B}+0.15q_{2C}&0.15q_{3B}+0.15q_{3C}&0.15q_{4B}+0.15q_{4C}\end{array}\right)[/tex]Therefore, UQ has 4 columns and 3 rows.
The 4 columns of UQ list the total costs for materials(Row 1), labor(Row 2), and overhead(Row 3) used to manufacture products B and C during the 4 quarters of the year.
How many different ways can the letters of "kissing" be arranged?
Answer:1260
Step-by-step explanation:
Kissing has 7 letters, and there are 2 paris of the same letter.
[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260
Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.
Answer:
r = -10*cos(t)
Step-by-step explanation:
To write the rectangular equation in polar form we need to replace x and y by:
[tex]x=r*cos(t)\\y=r*sin(t)[/tex]
Replacing on the original equation, we get:
[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]
Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:
[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]
In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random variable.
Answer:
The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.
Step-by-step explanation:
The question is incomplete:
The probability distribution is:
x P(x)
0 0.30
1 0.40
2 0.20
3 0.06
4 0.04
The mean can be calculated as:
[tex]M=\sum p_iX_i=0.3\cdot 0+0.4\cdot 1+0.2\cdot 2+0.06\cdot 3+0.04\cdot 4\\\\M=0+0.4+0.4+0.18+0.16\\\\M=1.14[/tex]
(pi is the probability of each class, Xi is the number of topping in each class)
The standard deviation is calculated as:
[tex]s=\sqrt{\sum p_i(X_i-M)^2}\\\\s=\sqrt{0.3(0-1.14)^2+0.4(1-1.14)^2+0.2(2-1.14)^2+0.06(3-1.14)^2+0.04(4-1.14)^2}\\\\s=\sqrt{0.3(-1.14)^2+0.4(-0.14)^2+0.2(0.86)^2+0.06(1.86)^2+0.04(2.86)^2}\\\\ s=\sqrt{0.3(1.2996)+0.4(0.0196)+0.2(0.7396)+0.06(3.4596)+0.04(8.1796)}\\\\s=\sqrt{0.3899+0.0078+0.1479+0.2076+0.3272}\\\\ s=\sqrt{ 1.0804 }\\\\s\approx 1.04[/tex]
Answer:
mean: 1.14; standard deviation: 1.04
Step-by-step explanation:
Which leader was a member of the Kikuyu tribe?
A. Kwame Nkrumah
B. Marcus Garvey
C. Mohandas Gandhi
D. Jomo Kenyatta
Answer:
Jomo Kenyatta
Step-by-step explanation:
Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.
Answer:
Jomo Kenyatta
Step-by-step explanation:
took the test
What number should go in the space? Multiplying by 0.65 is the same as decreasing by _____%
Answer: 35%
Step-by-step explanation:
If no is 10, 10 x 0.65 = 6.5. OR
10 - 35% of 10 = 6.5
Multiplying by 0.65 is the same as decreasing by 35%
Conversion of statements into algebraic expression:To convert the statement into algebraic expression choose the variables first.Then form the expression or equation as per given statements.
Let the number is 'a' and percentage decrease is 'b',
Expression for the given statement will be,
a × 0.65 = a - (b% of a)
[tex]0.65a=a(1-\frac{b}{100})[/tex]
[tex]0.65=1-\frac{b}{100}[/tex]
[tex]\frac{b}{100}=1-0.65[/tex]
[tex]b=100(0.35)[/tex]
[tex]b=35[/tex]
Therefore, Multiplying by 0.65 is the same as decreasing by 35%.
Learn more about the Algebraic expressions for the statements here,
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Tyler drew a figure that has two pairs of equal sides, four angles formed by perpendicular lines, and two pairs of parallel sides. What geometric term best describes the figure Tyler drew? What geometric term best describes the figure Tyler drew?
Answer:
A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.
Which of the following verified the triangle COW is similar to triangle PIG? Ignore the answer I filled in I didn’t meant to pick that one.
Answer:
D. SSS theorem
Step-by-step explanation:
The triangles have similarity by 3 sides:
4/12=5/15=7/21So the answer is SSS
What is the ratio 16 : 12 in its simplest form?
Answer:
4 : 3
Step-by-step explanation:
16 : 12 can be simplified by 4 to get 4 : 3
Answer:
[tex]4:3[/tex]
Step-by-step explanation:
[tex]16 : 12[/tex]
The common highest factor of the ratio is 4.
Simplify the ratio.
[tex]16 \div 4:12 \div 4[/tex]
[tex]4:3[/tex]
A box is 24 inches long, 10 inches wide, and 10 inches deep. About how many cubic feet is the box?
Answer:
1.3888888 ft^3
Step-by-step explanation:
We need to find the volume
V = l*w*h
V = 24*10*10
V =2400 in^3
We want cubic ft
Divide by 12 for each foot
12*12*12 = 1728 ft^3
2400/1728 =1.3888888 ft^3
Answer:
[tex] = 1.388889 {ft}^{3} [/tex]
Step-by-step explanation:
[tex]v = whl \\ = 10 \times 24 \times 10 \\ = 2400 {in}^{3} [/tex]
we know that,
[tex]1 \: \: in = 0.833333ft \\ x = 2400 \\ use \: \: cross \: \: \: multipication \\ 2400 = 0.833333x \\ \frac{2400}{0.833333} = \frac{0.833333x}{0.833333} \\ x = 1.388889 {ft}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Evelyn pets the box with 1 inch cubes with represents does not show how evelyn can’t find the volume of the box
Question Correction
Evelyn packed this box with 1 inch cubes. Which expression does not show how Evelyn can find the volume of the box?
(A)6+6+6+6+6+6 (B) 2 X 3 X 6 (C) 2 + 3 + 6 (D) 6 X 6Answer:
(C) 2 + 3 + 6
Step-By-Step Explanation
In the diagram,
Height = 6 Units Length =2 Units Width =3 UnitsVolume = Height X Length X Width
= 6 X 2 X 3
=36 cubic units
Consider the options:
(A)6+6+6+6+6+6 =36 cubic units
(B) 2 X 3 X 6 =36 cubic units
(C) 2 + 3 + 6 = 11 cubic units
(D) 6 X 6 =36 cubic units
Out of the option, that which is not equivalent to 36 cubic units is:
(C) 2+3+6
Therefore, it does not show how Evelyn can find the volume of the box.
Answer:
2+3+6
Step-by-step explanation:
i just did it
Anthony brought an 8 -foot board. He cut off 3/4 of the board to build a shelf and gave 1/3 of the rest to his brother for an art project. How many inches long was the piece Anthony gave to his brother?
Answer: 7.2 inches
Step-by-step explanation:
3/4th of 8 feet = 6 ft.
Balance = 2 feet
1/3 of 2 feet = 2/3 = 0.67 ft = 8 inches
deandre saves rare coins. he starts his collection with 14 coins and plans to save 3 coins each month. write an equation to represent the number of coins saved, y, in terms of the number of months, x. if deandre saved for 30 months, how many coins will he have?
Answer:
equation: y = 3x + 14
number of coins after 30 months: 104 coins
Hope this helps :)
An equation is formed of two equal expressions. The number of coins that will be with Deandre after a period of 30 months is 104 coins.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
As it is given that in the initial phase Deandre saves 14 coins. While he adds 3 coins each month. Therefore, the equation that will represent the number of coins that Deandre will have after a period of x months can be written as,
y = 14 + 3x
where y is the number of coins and x is the number of months.
After a period of x=30 months, the number of coins that will be with Deandre can be written as,
[tex]y = 14 + 3x\\\\y = 14 + 3(30)\\\\y = 104[/tex]
Thus, the number of coins that will be with Deandre after a period of 30 months is 104 coins.
Learn more about Equation:
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If the denominator of 5/9 is increased by a number and the numerator is doubled, the result is 1. Find the number.
◇Given :-
The denominator of a fraction is increased by a number and numerator will be doubled
To find
We have to find the required number or fraction
[tex]\underline{\bigstar{\sf\ \ Solution:-}}[/tex]
Now let us consided as the number be a
Then
[tex]\underline{\bigstar{\textit\ According\ to \ Question:-}}[/tex]The given fraction is 5/9
[tex]:\implies\sf \dfrac{5\times 2}{9+a}= 1\\ \\ \\ :\implies\sf \dfrac{10}{9+a}=1\\ \\ \\ :\implies\sf 10= 1(9+a)\\ \\ \\ :\implies\sf 10-9=a\\ \\ \\ :\implies\sf 1=a [/tex]
[tex]\underline{\therefore{\textit{\textbf { The \ required \ number \ is \ 1}}}}[/tex]⅝ of a school's population are girls. There are 129 boys. If each classroom can hold 25 students. How many classroom does the school have ?
Answer:
AT least 14 classrooms to hold the total number of students
Step-by-step explanation:
Since we don't know the numer of girls in the school, let's call it "x".
What we know is that the number of girls plus the number of boys gives the total number of students. This is:
x + 129 = Total number of students
Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:
"5/8 of the school's population are girls" as:
0.625 (x + 129) = x
then we solve for "x":
0.625 x + 0.625 * 129 = x
0.625 * 129 = x - 0.625 x
80.625 = x (1 - 0.625)
80.625 = 0.375 x
x = 80.625/0.375
x = 215
So now we know that the total number of students is: 215 + 129 = 344
and if each classroom can hold 25 students, the number of classroom needed for 344 students is:
344/25 = 13.76
so at least 14 classrooms to hold all those students
The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = − 26400 e − 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent.
Answer:
Step-by-step explanation:
Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation
V ' ( t ) = − 26400 e^− 0.49 t .
t = time (in days)
.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:
V'(6) = − 26400 e− 0.49 (6)
V'(6) = -26400e-2.94
V'(6) = -26400×-0.2217
V'(6) = $5852.88
V'(6) = $5,853 to nearest dollars
V'(6) = 585300cents to nearest cent
To get v(6), we need to get v(t) first by integrating the given function as shown:
V(t) = ∫−26400 e− 0.49 t dt
V(t) = -26,400e-0.49t/-0.49
V(t) = 53,877.55e-0.49t + C.
When t = 0, V(t) = $170,000
170,000 = 53,877.55e-0 +C
170000 = 53,877.55(2.7183)+C
170,000 = 146,454.37+C
C = 170,000-146,454.37
C = 23545.64
V(6) = 53,877.55e-0.49(6)+ 23545.64
V(6) = -11,945.63+23545.64
V(6) = $11,600 (to the nearest dollars)
Since $1 = 100cents
$11,600 = 1,160,000cents
c) Consider the time 3:40pm where the initial side is the hour hand and terminal side is the
minute hand. Draw the angle between the two hands in standard position. State the angle in
positive degrees and then restate the angle as a negative angle. (2 pts.)
Answer:
210 degrees-150 degreesStep-by-step explanation:
When the time is 3:40pm
The Initial Side (hour hand) is at 3.Terminal Side (Minute hand) is at 8.(a)The angle between the two hands in standard position is drawn and attached below.
(b)Now, each hour = 30 degrees
Therefore, the angle between 3 and 8 in an anticlockwise movement
= 7 X 30 =210 degrees
Stating the angle as a negative angle, we have:
[tex]210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ[/tex]
A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.a. P(A ∩ B).b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.
Complete question is;
A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.
a. P(A ∩ B).
b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.
Answer:
A) 0.4
B) 0.4
Step-by-step explanation:
We are given;
P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8
A) To solve this question, we will use the the general probability addition rule for the union of two events which is;
P(A∪B) = P(A) + P(B) − P(A∩B)
Making P(A∩B) the subject of the equation, we have;
P(A∩B) = P(A) + P(B) − P(A∪B)
Thus, plugging in the relevant values, we have;
P(A∩B) = 0.7 + 0.5 - 0.8
P(A∩B) = 0.4
B)The probability that the lifeline usage amount is exceeded in exactly one of the two months can be described in terms of A and B as:
P(A but not B) + P(B but not A) = P(A∩B') + P(B∩A')
where;
A' is compliment of set A
B' is compliment of set B
Now,
P(A∩B') = 0.7 − 0.4 = 0.3
P(B∩A') = 0.5 − 0.4 = 0.1
Thus;
P(A but not B) + P(B but not A) = 0.1 + 0.3 = 0.4
European car company advertises that their
car gers 9.4 Kilometers per liter of gasoline. Convert
this figure to miles per galllon
Answer:
22.11 miles per gallon
Step-by-step explanation:
1 km = 0.621371 miles
1 litre = 0. 264172 gallon
Given
Mileage of car = 9.4 Milometers per liter of gasoline
Mileage of car = 9.4 Km/ litres
now we will use 0.621371 miles for Km and 0. 264172 gallon for litres
Mileage of car = 9.4 * 0.621371 miles/ 0. 264172 gallon
Mileage of car = 9.4 * 2.3521 miles/ gallon
Mileage of car = 22.11 miles/ gallon
Thus, 9.4 Km/litres is same as 22.11 miles per gallon.
Working together Wayne and his son Garth can mow the lawn in 30 min, but if Wayne mow the lawn alone then it takes 1h 15min. Find how long does it take for Garth to mow their lawn if he does it alone.
Answer:
105
Step-by-step explanation:
1h and 15 minutes is 75 minutes so
30+75=
70+30=100
100+5=105
Answer:
105
Step-by-step explanation:
I copied the other dude
3. How many different arrangements can be made with the letters in the word
POWER?
O A 100
B 25
OC 20
OD 120
Answer:
D. 120
Step-by-step explanation:
Array formula: A (n, p) = n! / (n -p)!
At where:
n = Total number of elements in the set.
p = Quantity of elements per arrangement
A (5.5) = 5! / (5-5)! = (5x4x3x2x1) / 0!
By definition: 0! = 1
Then: 120/1 = 120
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.55 inches.
Required:
a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
b. What percentage of men are SHORTER than 6 feet 3 inches?
c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
d. What percentage of women are TALLER than 5 feet 11 inches?
Answer:
a) 1.93
b) 97.32% of men are SHORTER than 6 feet 3 inches
c) 2.71
d) 0.34% of women are TALLER than 5 feet 11 inches
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
For man, [tex]\mu = 69.8, \sigma = 2.69[/tex]
A feet has 12 inches, so this is Z when X = 6*12 + 3 = 75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 69.8}{2.69}[/tex]
[tex]Z = 1.93[/tex]
b. What percentage of men are SHORTER than 6 feet 3 inches?
Z = 1.93 has a pvalue of 0.9732
97.32% of men are SHORTER than 6 feet 3 inches
c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
For woman, [tex]\mu = 64.1, \sigma = 2.55[/tex]
Here we have X = 5*12 + 11 = 71.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{71 - 64.1}{2.55}[/tex]
[tex]Z = 2.71[/tex]
d. What percentage of women are TALLER than 5 feet 11 inches?
Z = 2.71 has a pvalue of 0.9966
1 - 0.9966 = 0.0034
0.34% of women are TALLER than 5 feet 11 inches
Can anyone help me with the answer please
Answer:
All real numbers
Step-by-step explanation:
The domain is where the graph touches all of the x-coordinates. This parabola touches all x-coordinates from -infinity to +infinity (all real numbers) because it continues outward forever.
Answer: all real numbers
Step-by-step explanation:
The domain is how many x values are possible, but there is no limit to that, it is infinite. So the domain is all real numbers.
The line of reflection is the ____. y-axis, center of rotation, x-axis
Answer:The line of reflection is the y axis
Step-by-step explanation:
P(AB) can be read as "the probability that A occurs given that Bhas
occurred."
A. True
B. False
Answer:
False
Step-by-step explanation:
from *millermoldwarp*
"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."
hopes this helps
Answer:false
Step-by-step explanation: