Answer:
7.3%
Step-by-step explanation:
Let M = Maths
E = English
P(M ∪ E) = P(M) + P(E) - P( M ∩ E)
From the question:
P(M ∪ E) = 35.7%
P(M) = 18%
P(E) = 24%
P( M ∩ E) = unknown
35.7% = 18% + 24% - P( M ∩ E)
35.7% = 42% - P( M ∩ E)
P( M ∩ E) = 42% - 35.7%
P( M ∩ E) = 7.3%
Therefore, the probability that a student who receives an A in Math course will also receive an A in English course is 7.3%.
(pic inside) What is the approximate value of the function at x = -1? is it -2, -4, -3, or -1?
Answer:
y = - 4
Step-by-step explanation:
Locate x = - 1 then follow the line down until it meets the curve and read the corresponding value on the y- axis at this point.
For x = - 1, y = - 4
the average of two numbers is 11. the difference between is 4 , find the sum of the two numbers
please help
Answer:
22
Step-by-step explanation:
Let the first number be x.
Let the second number be y.
(x+y)/2 = 11
x-y=4
Solve for x in the second equation.
x = 4 + y
Put x as 4 + y in the first equation and solve for y.
(4+y+y)/2 = 11
4 + 2y = 22
2y = 18
y = 9
Put y as 9 in the second equation and solve for x.
x = 4 + 9
x = 13
Find the sum of the numbers x and y.
x + y
13 + 9
= 22
Answer:
[tex]22[/tex]
Step-by-step explanation:
let the numbers be x and y
[tex] \frac{x + y}{2} = 11 \\ x - y = 4[/tex]
so,
[tex] \frac{x + y}{2} = 11 \\ x +y = 11 \times 2 \\ x + y = 22[/tex]
So they asked to find the sum of the two numbers
And the answer is 22
What is the actual distance, in miles, between two cities that are 3 inches apart on the map?
Answer:
Step-by-step explanation: to answer this question I need to know what 1 inch to a mile is. like every one inch= 12 miles
He length of an alligator in a zoo is 14 5/8 feet. The everglades national park lists the longest alligator ever recorded in florida at 17 5/12 feet. Which is the difference in their lengths?
Answer:
2 and 1/6 feet
Step-by-step explanation:
To do this you would just put aside 17 and 14 and you would subtract 5/12 by 5/8. To subtract these you would just find the lcm which is 48 and that would be denominator and to make the top the same as the bottom you would just multiply how much it took the denominator and multiply the numerator. So to subtract them you would get 20/48 for 5/12 and 30/48 for 5/8. When you subtract them you get -10/12 so then you will subtract 17 and 14 which is 3 then you will subtract 3 - 10/12 and you would get 2 and 2/12 which can simplify to 2 1/6 feet
The difference in the lengths of alligators in zoos and Florida is 2.79 feet.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Given that
The length of an alligator in a Zoo = 14 5/8 feet.
The length of an alligator in Florida = 17 5/12 feet.
Convert fractions into decimals, and we get
The length of an alligator in a Zoo = 14.625 feet.
The length of an alligator in Florida = 17.416 feet.
So the difference in their lengths = 17.416 - 14.625
So the difference in their lengths = 2.79 feet
Therefore, the difference in the lengths of alligators in zoos and Florida is 2.79 feet.
Learn more about Arithmetic operations here:
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Which pair of triangles can be proven congruent by SAS?
Note how the triangles here have the angles between the marked sides. The tickmarks indicate which pair of sides are the same length. The SAS sequence has "A" in the middle of the two "S" letters to mean that the angles are between the sides.
------------
Extra info:
For choice A, we have SSA going on but that isn't a valid congruence theorem. There isn't enough info to say whether the triangles are congruent or not.With choice B, we have three pairs of angles that are the same measure. We don't have any info about the sides though. So we can't say if the triangles are congruent or not. The AA (angle angle) theorem only applies to similar triangles rather than congruent triangles.The first pair of triangles can be proven congruent by SAS.
What is SAS postulate?SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.
Here, we have,
In the first pair of triangles the included angle of a triangle are equal to two sides and the included angle of another triangle, therefore by SAS postulate the two triangles are said to be congruent.
In the second figure, the pair of triangles are congruent by ASA postulate not SAS.
In the third figure, the pair of triangles are not congruent by any postulate or theorem [Because there is no SSA rule].
In the fourth figure, the pair of triangles are congruent by SSS postulate not SAS.
Hence, The first pair of triangles can be proven congruent by SAS.
learn more on congruent click:
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Use the Cross Products Property to solve the proportion
5/n =16/32
Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
If we have our proportion set up like this:
[tex]\frac{5}{n} = \frac{16}{32}[/tex]
Then using the cross products property, we can find the value of n.
The property states that the two numbers that are diagonal to each other DIVIDED by the number diagonal to the variable will equal the variable.
So:
[tex]32\cdot5 = 160\\160\div16 = 10[/tex]
Hope this helped!
how to do this question plz
Answer:
17.7 percent
Step-by-step explanation
You find the area of the trapezoid and rectangle. You divide the area of the trapezoid by the rectangle. then move the decimal 2 places to the right.
Agrid shows the positions of a subway stop and your house. The
subway stop is located at (-7,8) and your house is located at (6,4).
What is the distance, to the nearest unit, between your house and
the subway stop?
Answer: about 13u
Step-by-step explanation:
Distance can be calculated as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(6-(-7))^2+(4-8)^2}\\\\\\\sqrt{(13)^2+(-4)^2}\\\\\\\sqrt{185}\\\\13[/tex]
Hope it helps <3
The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triangle is 58 units. Which best describes the resulting three-dimensional shape?
Answer:
The new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.
Step-by-step explanation:
The image related to the exercise is necessary, to be able to solve therefore the attached one.
We have the following information:
Perimeter of the triangle = 58 units
Hypotenuse = 24 units
We have that the other two sides are equal and have x units, therefore we have the following:
x + x + 24 = 58
2 * x = 58-24
2 * x = 34
x = 34/2
x = 17
Now the triangle rotates around line k , and then it will result in a cone, which is a three-dimensional shape.
Therefore, the new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.
Answer:
Cone with a radius of 17 units
Darion saved the amount shown from his weekly allowance Calculate
the total amount he save 20$ 10$ 5$ 25$ 25$
Answer:
$20 i think
Step-by-step explanation: have a good day bye bye yup yup
What is the slope of the following line? Be sure to scroll down first to see all answer options. (-2, 11) (2, -3)
Answer:
-7/2
Step-by-step explanation:
We can find the slope by using the slope formula
m = (y2-y1)/(x2-x1)
= ( -3 -11)/( 2- -2)
= ( -14)/ ( 2+2)
= -14/4
= -7/2
Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
Answer:
The correct option is;
A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25
Please find attached the graphs of the table data
Step-by-step explanation:
Each of the given table data of in the tables are analysed to find direct variation;
Table 1
x, -3, -1, 2, 5, 10
y, -4.5, -3.0, -1.5, 0.0, 1.5
-4.5/-3 = 1.5 ≠ -3.0/-1 = 3
No direct variation
Table 2
x, -5.5, -4.5, -3.5, -2.5, -1.5
y, 10, 8, 6, 4, 2
10/(-5.5) = -20/11 ≠ 8/(-4.5) = -16/9
However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2
Adjusted direct variation
Table 3
x, -5.5, -5.5, -5.5, -5.5, -5.5
y, -3, -1, 2, 5 , 10
-3/(-5.5) ≠ -1/-5.5
No direct variation
Table 4
x, -3, -1, 2, 5, 10
y, -7.5, -2.5, 5.0 , 12.5, 25
-7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10
Direct variation exists
Answer:
so D
Step-by-step explanation:
Volume of a Triangular Prism
Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Answer:
Volume of prism = 240 ft²
Step-by-step explanation:
Given:
Base of prism (B) = 10 ft
Length of prism (L) = 8 ft
Height of prism (H) = 6 ft
Find:
Volume of prism
Computation:
Volume of prism = [BHL] / 2
Volume of prism = [(10)(8)(6)] / 2
Volume of prism = [480] / 2
Volume of prism = 240 ft²
simplify √16n/m^3 1. 4√mn/n^2 2. 4√mn/m 3. √mn/4m 4. 4√mn/m^2
Answer:
4√mn/m^2
Step-by-step explanation:
√16n/m^3
= √16n/√m^3
= √4x4xn/√mxmxm
= 4√n/m√m
Rationalize by multiplying the numerator and the denominator by the denominator, which is a surd:
= (4√n x √m)/(m√m x √m)
= 4√mxn/m√mxm
= 4√mn/mxm
= 4√mn/m^2
simplify 8a-5b-(6a-9b)
Answer:
2(a + 2b)Step-by-step explanation:
[tex]8a - 5b - (6a - 9b)[/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression.
[tex]8a - 5b - 6a + 9b[/tex]
Collect like terms
[tex]2a + 4b[/tex]
Factor out 2 from the expression
[tex]2(a + 2b)[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
2(a + 2b)
Step-by-step explanation:
Question 21 of 31
What is the length of AC?
Answer:
C. 126
Step-by-step explanation:
We can use ratios to solve for corresponding side lengths.
[tex]\frac{140-x}{81} =\frac{x}{9}[/tex]
Cross multiply.
[tex]9(140-x)=81x[/tex]
[tex]140-x=9x[/tex]
[tex]140=10x[/tex]
[tex]14=x[/tex]
Plug x as 14.
[tex]140-14=126[/tex]
Find the dimensions of a deck which will have railings on only three sides. There is 28 m of railing available and the deck must be as large as possible.
Answer:
2x2x7
Step-by-step explanation:
A combination lock has 6 different numbers. If each number can only be used ONCE, how many different combinations are possible?
Answer:
151200 possible combinations
Step-by-step explanation:
There are 10 digits 0 - 9 ( 0,1,2,3,4,5,6,7,8,9)
There are 10 choices for the first digit
10
There are 9 choices for the second digit
9
There are 8 choices for the third digit
8
and so on since we can only use each digit once
10 *9*8 *7 *6*5
151200 possible combinations
Please answer this question now in two minutes
Answer:
20
Step-by-step explanation:
use the cos or sin function to solve
Step-by-step explanation:
using 30°
we use cos
cos 30 =10√3/UU = 10√3/Cos30 =20cmusing 60
we use Sin
Sin 60=10√3/UU = 10√3/Sin60 = 20A certain ferry moves up and down a river between Town A and B. It takes the ferry two hours to travel to Town A and only an hour and thirty minutes to return to Town B. If the current is 5mph how far apart are the two cities?
Answer:
The distance between two cities is 60 miles.
Step-by-step explanation:
Time taken to travel from B to A = 2 hours
Time taken to travel from A to B = 1.5 hours
Current speed = 5 mph
Let the speed of ferry in still water = u mph
When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).
Let the distance between the two cities A and B = D miles
While moving with the current, speed = [tex](u+5)\ mph[/tex]
While moving against the current, speed = [tex](u-5)\ mph[/tex]
Formula for Distance = Speed [tex]\times[/tex] Time
Distance traveled in each case is same i.e. D.
So,
[tex]D = (u+5) \times 1.5 = (u-5) \times 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = \dfrac{175}{5}\\\Rightarrow u = 35 \ mph[/tex]
Now,
[tex]D = (u+5) \times 1.5\\\Rightarrow D =(35+5) \times 1.5\\\Rightarrow D =(40) \times 1.5\\\Rightarrow \bold{D =60\ miles}[/tex]
So, the distance between two cities is 60 miles.
Answer:
I believe that the answer is 60 miles
Step-by-step explanation:
Please answer the following questions
Answer:
4a) 110 square centimetres
4b) 127 square centimetres
6) 292 square centimetres
8) 800 tiles
Step-by-step explanation:
4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:
a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:
A = 12 * 15 = 180 square centimetres
The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:
a = 10 * 7 = 70 square centimetres
Therefore, the area of the shaded part is:
A - a = 180 - 70 = 110 square centimetres
b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:
A = 13 * 11 = 143 square centimetres
The unshaded part has dimensions 8 cm by 2 cm. Its area is:
a = 8 * 2 = 16 square centimetres
Therefore, the area of the shaded part is:
A - a = 143 - 16 = 127 square centimetres
6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.
The frame has dimensions 24 cm by 18 cm. Therefore, its area is:
A = 24 * 18 = 432 square centimetres
The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:
a = 14 * 10 = 140 square centimetres
Therefore, the background area of the space not covered by the photograph is:
A - a = 432 - 140 = 292 square centimetres
8) The floor has dimensions 8 m by 4 m. The area of the floor is:
A = 8 * 4 = 32 square centimetres
Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:
a = 0.2 * 0.2 = 0.04 square metres
The number of tiles that are needed is the area of the floor divided by the area of each tile:
A / a = 32 / 0.04 = 800 tiles
1.5 rounded to the nearest one
Answer:
2
Step-by-step explanation:
Five and above, round up. Four and below, round down.
Answer:
2
Step-by-step explanation:
anything less then five is rounded down anything above 5 is rounded to the higher number
AB and BC form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of BC?
A. x + 3y = 16
B. 2x + y = 12
C. -7x − 5y = -48
D. 7x − 5y = 48
===============================================
First we need the equation of line AB. Compute the slope through (-3,-1) and (4,4)
m = (y2-y1)/(x2-x1)
m = (4-(-1))/(4-(-3))
m = (4+1)/(4+3)
m = 5/7
This is the slope through points A and B, ie the slope of line AB.
To get the slope of line BC, we flip the fraction and change the sign.
Doing so has us go from 5/7 to -7/5. Note how 5/7 and -7/5 multiply to -1.
The slope of line BC is -7/5. Let m = -7/5.
--------
Use (x,y) = (4,4) along with m =-7/5 to find the equation of line BC
y = mx+b
4 = (-7/5)(4) + b
4 = -28/5 + b
20 = -28 + 5b ... multiply every term by 5 to clear out the fraction
20+28 = 5b
48 = 5b
5b = 48
b = 48/5
With m = -7/5 and b = 48/5, we go from y = mx+b to y = (-7/5)x+48/5
The slope intercept form for line BC is y = (-7/5)x+48/5
--------
Let's get this into standard form Ax+By = C
y = (-7/5)x+48/5
5y = -7x + 48 .... multiply everything by 5
7x+5y = 48 .... is one way to represent the equation in standard form
-7x - 5y = -48 ... your teacher has decided (for some reason) to multiply both sides by -1
Answer:
-5y-7y=-48
Step-by-step explanation:
distance between BC (4,4) C(x,y)
BC is perpendicular on AB (perpendicular line has opposite reciprocal slope)
slope of AB=y2-y1/x2-x1=4-(-1)/4-(-3)=5/7
slope of BC=-7/5
now input the value of B (4.4) and C(x,y)
y=mx+b
4=-7/5(4)+b
b=4+28/5
b=48/5
y=-7/5x+48/5
5y=-7x+48
5y+7x=48 multipy by -1
-5y-7y=-48
PLZZ HEPPP A line passes through (−1, 5) and (1, 3). Which answer is the equation of the line? x + 2y = 7 x + y = 4 x + 2y = 5 x + y = 2
Answer:
B.
Step-by-step explanation:
Again, to find the equation of the line, we need to find the slope and y-intercept. First, let's find the slope. Let (-1,5) be x₁ and y₁ respectively and (1,3) be x₂ and y₂, respectively. So:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{1--1}=\frac{-2}{2}=-1[/tex]
So the slope is -1.
Now, to find the y-intercept, we can use the point-slope form. I'm going to keep using (-1,5) as the coordinate. Thus:
[tex]y-y_1=m(x-x_1)\\y-5=-1(x-(-1))\\y-5=-(x+1)\\y-5=-x-1\\y=-x+4[/tex]
This is slope-intercept form. We want the answer to be in standard form, where:
[tex]Ax+By=C[/tex]
A, B, and C are integers (and, conventionally, A is positive).
Thus, we need to rearrange the terms:
[tex]y=-x+4\\y+x=4\\x+y=4[/tex]
The answer is B.
If one- tenth of a number is added to 2, the result is half of that number, find the number. A. 2.5 B. 3.3 C. 4.2 D. 5.0
Answer:
D. [tex]\boxed{x = 5}[/tex]
Step-by-step explanation:
Let the number be x
Condition:
[tex]\frac{1}{10} x + 2 = \frac{1}{2} x[/tex]
[tex]\frac{x}{10} -\frac{x}{2} = -2\\LCM = 10\\Multiplying \ both \ sides \ by \ 10\\x - 5(x) = -2(10)\\x -5x = -20\\-4x = -20[/tex]
Dividing both sides by -4
x = 5
Answer:
[tex]\boxed{5.0}[/tex]
Step-by-step explanation:
Let the number be [tex]x[/tex].
1/10 of x is added to 2, the result is half of x.
[tex]2+\frac{1}{10} x=\frac{1}{2} x[/tex]
[tex]2=\frac{1}{2} x-\frac{1}{10} x[/tex]
[tex]2=\frac{2x}{5}[/tex]
[tex]10=2x[/tex]
[tex]\frac{10}{2} =x[/tex]
[tex]5=x[/tex]
The number is 5.0
Lines m and n are parallel. Which of the other 5 named angles have a measure of 110°?
Press the hotspot for all that apply.
2 bcoz vertically opp
the one in front of 3, I can't see that number maybe 4
because corresponding angles
yea that's all
Simplify completely quantity 3 x plus 18 over 18
Answer:
(x+6) / 6
Step-by-step explanation:
(3x+18) /18
Factor out 3 from the numerator
3(x+6) /18
Cancel a 3 from the numerator and denominator
(x+6) / 6
A plane traveled 5525 miles with the wind in 8.5 hours and 4505 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is ____(hours.miles.mph) (Simplify your answer.)
Answer:
590mph
Step-by-step explanation:
Speed with wind = 5525÷ 8.5
= 650mph
speed against wind = 4505÷8.5
= 530mph
speed without wind = (650mph+530mph)÷2
= 590mph
factor the equation. x2-15x+54=0
Answer:
I hope it will help you...
Answer:
(x-9)(x-6)
x= 9, x= 6
Step-by-step explanation:
x² - 15x + 54 = 0x² - 9x - 6x + 54 = 0x(x-9) - 6(x-9)= 0(x-9)(x-6)= 0Factored, and roots are:
x-9=0 ⇒ x= 9x- 6 =0 ⇒ x= 6A cryptarithm is a math puzzle in which the digits in a simple equation are replaced with letters. Each digit is represented by only one letter, and each letter represents a different digit. So, for example, we might represent 51+50 = 101 as AB + AC = BCB. In the cryptarithm} SEND + MORE = MONEY, what digit does the letter Y represent?
Answer:
y=2
Step-by-step explanation:
SEND + MORE = MONEY
notice that send and more have 4 digit ( means the number in thousands ,but the answer is 5 digit means it is in 10000)
first word : 1000S+100E+10N+1 D
second word: 1000 M +100 O+10 R+1 E
the answer: 10000M+1000O+100N+10E+Y
if the answer is the sum of first word+second word:
(S E N D M O R E Y)
M in word Money can not be zero the range is [1,9]
S also can not be zero
S E N D s=9 since E can not equal N it has to be 1+E=N
9 5 6 7
+
M O R E m=1 , then o =0
1 0 8 5
M O N E Y
1 0 6 5 2