Answers
Answer:
(5, 7.8)
Step-by-step explanation:
There are several ways to solve this problem, but all of them involve similar triangles and ratios.
See the attached image.
The horizontal distance between points D and E is 11 - 1 = 10. If a segment 10 units long is divided in the ratio 2:3 (as shown by the two smaller segments of length a and b), then
[tex]\frac{a}{b}=\frac{2}{3}\\\frac{a}{a+b}=\frac{2}{2+3}\\\frac{a}{10}=\frac{2}{5}[/tex]
"Cross-multiply" to get
5a = 20
a = 4
To get the x-coordinate of point G, add 4 to 1, the x-coordinate of D.
The x-coordinate of G is 1 + 4 = 5.
The same idea can be used on the second coordinate of G.
The vertical distance from D to E is 15 - 3 = 12.
[tex]\frac{a}{b}=\frac{2}{3}\\\frac{a}{a+b}=\frac{2}{2+3}\\\frac{a}{12}=\frac{2}{5}[/tex]
5a = 24
a = 24/5 = 4.8
The y=coordinate of G is 3 + 4.8 = 7.8
Related Questions
-7 2/3+ (-5 1/2)+ 8 3/4=
Answers
First rewrite the fractions to have a common denominator.
2/3 = 8/12 , 1/2 = 6/12 and 3/4 = 9/12
Now you have:
-7 8/12 + (-5 6/12) + 8 9/12
-7 8/12 + (-5 6/12) becomes -7 8/12 - 5 6/12 = -13 2/12
Now you have
-13 2/12 + 8 9/12 = -4 5/12
Answer: -4 5/12
Step-by-step explanation:
-7(⅔) + -5(½) + 8(¾)
-23/3 + (-11/2) + 35/4
-92 - 66 + 105/12
-154 + 105/12
-49/12
What is the image point of (-4,2)(−4,2) after a translation left 1 unit and down 2 units?
Answers
Answer
I think it's going to be (-5,0)
Step-by-step explanation:
1. What is the sample space if you roll two dice? What is the probability of rolling a sum of 7?
2. You and a friend go to a restaurant where you both order a soup and a salad. There are four soups (A, B, C, D) and 3
salads (1, 2, 3) to choose from. If you and your friend decide to get completely unique meals, what is the sample space
of possible orders you can make?
3. Give 3 examples of disjoint events.
4. The probability that Bob gets to work on time is 80%. The probability that Sarah gets to work on time is 90%. The
probability that they're both on time is 72%. What's the probability that Bob OR Sarah is late for work?
5. Jake's Pizza Place is offering a deal where they'll deliver your pizza in under 30 minutes or your pizza is free. They
manage to deliver the pizza in under 30 minutes 92% of the time. What's the probability that you'll get your pizza for
free?
6. The probability that a randomly selected student in our class likes soccer is 54%. If we select 3 random students
from our class, what is the probability that all of them like soccer?
7. The probability that a randomly selected student in our class likes soccer is still 54%. If we select 4 random students
from our class, what is the probability that all of them don't like soccer?
8. There are 6 blue marbles, 5 red marbles, and 4 green marbles in a box. If you pull a green marble out of the box, what
is the probability that the next marble you draw is red?
9.60% of students in a class studied for a test AND got an A on that test. 75% of students studied for the test. What is
the probability that a student got an A given that they studied for the test?
Answers
Probabilities are used to determine how likely it is for an event to happen.
(1) A roll of two dice
Let the dice be A and B. The sample space of each is:
[tex]A = \{1,2,3,4,5,6\}\\B = \{1,2,3,4,5,6\}[/tex]
To get the sample space (S) of the sum of the dice, we simply add up the individual element of both dice. So, we have:
[tex]S = \{(1+1),(1+2),(1+3),(1+4),(1+5),(1+6),.............,(6+1),(6+2),(6+3),(6+4),(6+5),(6+6)\}[/tex]
This gives
[tex]S = \{2,3,4,5,6,7,.............,7,8,9,10,11,12\}[/tex]
The complete sample space is:
[tex]S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12\}[/tex]
[tex]n(S) = 36[/tex] --- the total outcomes
The probability of rolling a sum of 7 is:
[tex]P(7) = \frac{n(7)}{n(S)}[/tex]
Where
[tex]n(7) = 6[/tex] ---- number of 7's in the sample space
So, we have:
[tex]P(7) = \frac 6{36}[/tex]
[tex]P(7) = 0.167[/tex]
The probability of rolling a sum of 7 is 0.167
(2) Restaurant
We have:
[tex]Soup = \{A,B,C,D\}[/tex]
[tex]Salads = \{1,2,3\}[/tex]
To get the sample space (S), we simply pick the individual elements of the above data. So, we have:
[tex]S = \{A1, A2, A3,B1, B2, B3,C1, C2, C3,D1, D2, D3\}[/tex]
(3) Disjoint events
Events are said to be disjointed if they cannot happen at the same time. 3 examples are:
Event 1: You are in China. Event 2: You are in NigeriaEvent 1: Heading towards north. Event 2: Heading towards southEven 1: Outcome of even number in a roll of die. Event 2: Outcome of an odd number in the same die(4) Bob and Sarah
Let
[tex]A \to[/tex] Bob gets to work on time
[tex]B \to[/tex] Sarah gets to work on time
[tex]P(A) = 80\% \\ P(B) = 90\%\\P(A\ n\ B) = 72\%[/tex]
The probability that Bob OR Sarah is late for work is represented as:
[tex]P(A'\ or\ B')[/tex]
This is calculated using:
[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]
Where:
[tex]P(A') = 1 - P(A) = 1 - 80\% = 20\%[/tex]
[tex]P(B') = 1 -P(B) = 1 - 90\% =10\%[/tex]
[tex]P(A\ n\ B') = P(A) \times P(B') = 20\% \times 10\% = 2\%[/tex]
So, we have:
[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]
[tex]P(A'\ or\ B') = 20\% + 10\% - 2\%[/tex]
[tex]P(A'\ or\ B') = 28\%[/tex]
[tex]P(A'\ or\ B') = 0.28[/tex]
The probability that Bob OR Sarah is late for work is 0.28
(5) Jake's Pizza
Let
[tex]A \to[/tex] The proportion of time they deliver on time
[tex]B \to[/tex] You get your pizza for free
So:
[tex]P(A) = 92\%[/tex]
You get your pizza for free if they didn't deliver within 30 minutes.
This means that:
[tex]P(B) = 1 - P(A)[/tex] --- Complement rule
So, we have:
[tex]P(B) = 1 - 92\%[/tex]
[tex]P(B) = 0.08[/tex]
The probability that you get your pizza for free is 0.08.
(6) Students and Soccer
Let:
[tex]A \to[/tex] Probability that a student likes soccer
So:
[tex]P(A) = 54\%[/tex]
If all 3 selected students like soccer, the probability is calculated as:
[tex]Pr = P(A) \times P(A) \times P(A)[/tex]
[tex]Pr = P(A)^3[/tex]
[tex]Pr = 54\%^3[/tex]
[tex]Pr = 0.157[/tex]
The probability that all 3 selected students like soccer is 0.157
(7) Students and Soccer
Let:
[tex]A \to[/tex] Probability that a student likes soccer
[tex]B \to[/tex] Probability that a student does not like soccer
So:
[tex]P(A) = 54\%[/tex]
[tex]P(B)= 1 - P(A)= 1 - 54\% = 46\%[/tex] ---- Complement rule
If all 4 selected students do not like soccer, the probability is calculated as:
[tex]Pr = P(B) \times P(B) \times P(B) \times P(B)[/tex]
[tex]Pr = P(B)^4[/tex]
[tex]Pr = 46\%^4[/tex]
[tex]Pr = 0.045[/tex]
The probability that all 4 selected students do not like soccer is 0.045
(8) Marbles
[tex]Blue = 6 \\ Green = 4 \\ Red = 5[/tex]
When the green marble is selected, we are left with
[tex]Blue = 6 \\ Green = 3 \\ Red = 5[/tex]
The probability of selecting a red marble at this point is:
[tex]P(Red) = \frac{Red}{Blue + Green + Red}[/tex]
[tex]P(Red) = \frac{5}{6+3+5}[/tex]
[tex]P(Red) = \frac{5}{14}[/tex]
[tex]P(Red) = 0.357[/tex]
The probability that the next marble you draw is red is 0.357
(9) Studying for test
Let
[tex]A \to[/tex] Students got an A
[tex]B \to[/tex] Students studied for test
So:
[tex]P(A\ n\ B) = 60\% \\ P(B) = 75\%[/tex]
The probability that a student got an A given that they studied for the test is represented as:
[tex]P(A | B)[/tex]
So, we have:
[tex]P(A | B) = \frac{P(A\ n\ B)}{P(B)}[/tex]
[tex]P(A | B) = \frac{60\%}{75\%}[/tex]
[tex]P(A | B) = 0.80[/tex]
The probability that a student got an A given that they studied for the test is 0.80
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The equation 2x^2 + x - 1 = 0 has two solutions. Find an equation of the form ax^2 + bx + c = 0, which solutions....
a) are by 5 larger
b) 3 time as large
Can someone please help me with this task? Thank you for your answers!
Answers
Answer:
Step-by-step explanation:
Let the solution to
2x^2 + x -1 =0
x^2+ (1/2)x -(1/2)
are a and b
Hence a + b = -(1/2) ( minus the coefficient of x )
ab = -1/2 (the constant)
A. We want to have an equation where the roots are a +5 and b+5.
Therefore the sum of the roots is (a+5) + (b+5) = a+ b +10 =(-1/2) + 10 =19/2.
The product is (a+5)(b+5) =ab + 5(a+b) + 25 = (-1/2) + 5(-1/2) + 25 = 22.
So the equation is
x^2-(19/2)x + 22 =0
2x^2-19x + 44 =0
B. We want the roots to be 3a and 3b.
Hence (3a) + (3b) = 3(a+b) = 3(-1/2) =-3/2 and
(3a)(3b) = 9(ab) =9(-1/2)=-9/2.
So the equation is
x^2 +(3/2) x -9/2 = 0
2x^2 + 3x -9 =0.
Sam has 2 apples and bob has 5 apples bob gives Sam 2 apples how many apples does bob have now?
Answers
Answer:
Bob has 3 apples
.......
-6|5-2y|=-9
Please answer this I need to pass this class
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
y = 7 4 , 13 4
Decimal Form:
y = 1.75 , 3.25
Mixed Number Form:
y = 1 3 4 , 3 1 4
Step-by-step explanation:
Answer:
y = 1.75
Step-by-step explanation:
y = 7/4
ghỹd7d6dlyyuz
9. The sum, Sn, of the first n terms of a geometric progression is given by Sn = 3" - 1.
(a) the sum of the first 8 terms.
Answers
[tex]\boxed{\sf S_n=3^n-1}[/tex]
Now
[tex]\\ \sf\longmapsto S_8=3^8-1[/tex]
[tex]\\ \sf\longmapsto S_8=6561-1[/tex]
[tex]\\ \sf\longmapsto S_8=6560[/tex]
solve v^2 = 47. need this answer asap
Answers
7^2 equals 49
The reason is because 7x7=49
Find the sum of all the integers from 1 to 100 inclusive that are not
Multiples of 7.
Answers
Step-by-step explanation:
[tex]\text{Denote The sum of all the integers from 1 to 100 inclusive that are NOT multiples of 7 as } S.[/tex]
[tex]\text{Denote The sum of all the integers from 1 to 100 inclusive that are multiples of 7 as } P.[/tex]
[tex]\text{Denote The sum of all the integers from 1 to 100 inclusive as } Q.[/tex]
Then
[tex]\begin{align}S&=Q-P\\&=\frac{100(100+1)}{2}-(7+2\cdot7+\ldots+14\cdot7)\\&=\frac{100(100+1)}{2}-7\cdot\frac{14(14+1)}{2}\\&=4315\end{align}[/tex]
Solve for the value of V
Answers
Answer:
0.362°
Step-by-step explanation:
hope this helps you
The value of v in the figure is 14
How to determine the value of v?The angles on a straight line add up to 180 degrees.
So, we have:
4v + 90 + 34 = 180
Subtract 90 from both sides
4v + 34 = 90
Subtract 34 from both sides
4v = 56
Divide both sides by 4
v = 14
Hence, the value of v in the figure is 14
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2. By finding the size of each exterior angle of a regular decagon, find the size of each interior angle of the decagon
Answers
Step-by-step explanation:
Every exterior is 360
So 36 for each exterior.
Decagon interior is 1440
So each interior angle is 144
Answer:
interior angle = 144°
Step-by-step explanation:
A decagon has 10 sides
The sum of the exterior angles of a polygon is 360° , then
exterior angle = 360° ÷ 10 = 36°
The sum of an exterior angle and an interior angle = 180° , then
interior angle = 180° - 36° = 144°
Candace is going to order 8 pizza cost $8.95. How much does it cost to buy 8 pizzas?
Answers
sin 0 = -3/5
and cos 0 > 0. Identify the quadrant of the terminal side of O and find cos 0.
Answers
Answer:
See below.
Step-by-step explanation:
Cos O is positive in the first and 4th quadrants and sin O is negative in the 3rd and 4th quadrants.
So the answer is Quadrant 4.
cos^2 O = 1 - sin^2 O
= 1 - (-3/5)^2
= 16/25
So cos O is +√(16/25)
= 4/5.
Solve the following inequality for q. Write your answer in simplest form.
4q+5 > 69 - 7
Answers
Answer:
4q + 5 > 69 - 7
4q + 5 > 62
4q > 47
q > 11.75
Answer:
q> 57/4
Step-by-step explanation: hope it helps
Pls help I’ll give 20 points
Hey A store pays 5%
commission on the first
$500 in sales and 7% on
sales over $500. Find
the commission on a
$950 sale,
Answers
Answer:
144$
Step-by-step explanation:
Which equation has the solution to x = 3?
A. 2x - 8 = 5
B. 9x + 4 = -3
C. 6x - 9 = 57
D. 5x - 9 = 6
Answers
it takes 4 people 2 days to build a wall. how long will it take for 2 poeple to build the same wall?
Answers
Which expression is equivalent to r9/r3?
Answers
r⁹/r³ = r⁶ (because 9 - 3 = 6)
a^m : a^n = a^{m - n}
Answer:
Option B. r ^ 6
Step-by-step explanation:
r^9 / r^3
= r ^ 9 - 3
= r ^ 6
What is the value of each missing angle (x)?
100
х
Х
100
Answers
Answer:
it is 80° if the sum of angels X & angel 100° is 180°
17.6x23
I need the work
Answers
Answer:
17.6 × 23 = 404.8
Step-by-step explanation:
hope u like it
Answer:
= 17.6 x 23 Answer = 404.8A man is three times as old as his son in 10 years time their combined ages will be 68 how old is each person now person now
Answers
Answer:
The dad is 36 and the son is 12
Solve for b
y=mx+b
Let me know
Answers
Answer:
the answer is A i think
Step-by-step explanation:
hope it helps
Answer: b = y - mx
Step-by-step explanation:
y = mx + b
subtract mx from both sides: y - mx = b
b = y - mx
5. Select All equations that have a solution of 2"
10 point
4x + 15 = 27
x +6
= 9
3
Option 1
U
Option 2
2(x + 5) = 18
x +9
= 6
2
O
Option 3
Option 4
Answers
Answer:
none of these have a solution of 2.
Step-by-step explanation:
4x+ 15 = 27
x=3
x + 6 =3
x = 3
2(x+5)=18
x = 4
x + 9 = 6
x = -3
if my understanding of what the equations are supposed to be please let me know what they are supposed to be, because with the way they are typed it is hard to tell :)
Evaluate -5x + 4
When x = -3
Answers
Answer:
19.
Step-by-step explanation:
-5x + 4
-5(-3) + 4
15 + 4
19
Hey there!
-5x + 4
= -5(-3) + 4
= 15 + 4
= 19
Therefore, your answer is: 19
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
2(3+m) AS A WORD PROBLEM!!!! :)
Answers
Answer:
twice the sum of a number and 3
Step-by-step explanation:
twice would be best represented for the 2 in 2(3 + m)
and the sum of a number is m and is being added by 3 so we call it the sum of a number and 3
On Friday the farmers market sold 26 pounds of apples. On Saturday they sold 7 times that amount. On Sunday they sold 32 pounds of apples. How many pounds of apples were sold over these 3 days?
Answers
Answer:
240
Step-by-step explanation:
26+(26×7)+32
26+182+32
208+32
240
In 3 days 240 pounds apples sold.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
On Friday= 26 pounds Apples sold.
On Saturday = 7 x 26= 182 pounds apples sold.
On Sunday = 32 pounds
Then, In three days total pounds of apples sold
= 26 + 182 + 32
= 240 pounds
Hence, in 3 days 240 pounds apples sold.
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Which of the following is equal to the opposite of −45?
Answers
Answer:
45?
I gots no idea?
Answer:
45
Step-by-step explanation:
Opposite refers to differing signs but the same distance from 0.
Answer the question please
Answers
A scale dilation by a factor of 2 means that everything (both x and y coordinates) will be twice as big.
So multiply each coordinate by 2 and what do you get?
check weather 6x2-5x - 14 is exactly divisible by (x-2) or not
Answers
Answer:
[tex]\large \boldsymbol {} 6x^2 -5x-14 =0 \\\\ D=25+14\cdot 4\cdot 6 =361=19^2 \\\\ x_1= \dfrac{5+19}{12} =2 \\\\\\ x_2 =\dfrac{5-19}{12} =-\dfrac{7}{6} \\\\ and \ \ we \ \ \ know \ \ that \\\\\ 6x^2 -5x-14 =6 (x-x_1) ( x- x_ 2) = 6 ( x-(-\frac{7}{6} ))\boldsymbol { ( x-2 ) } \\\\ as \ we \ can \ see \ , \ the \ \ expansion \ is \\\\\ x-2 ; therefore \ \ , \ \ the \ \ answer \ \ is \ \ yes[/tex]
Answer: Yes: divisible
Step-by-step explanation:
[tex]P(x)=6x^2-5x-14\\\\P(2)=6*2^2-5*2-14=24-10-14=0\\\\P(x)\ is\ exactly\ divisible\ by\ x-2\\[/tex]
Solve for x. fx - gx = h
Answers
Answer:
x = h / f - g
Step-by-step explanation:
fx−gx = h
x(f−g) = h
/ (f-g) / (f-g) divide both sides by (f−g)
---------------------
x = h / f - g
The solution for x in the given equation is x = h / (f - g).
To solve for x in the equation fx - gx = h, we need to isolate the variable x.
First, to combine like terms on the left side of the equation.
fx - gx can be rewritten as (f - g)x.
So the equation becomes (f - g)x = h.
Next, to isolate x, we can divide both sides of the equation by (f - g).
x = h / (f - g).
Therefore, the solution for x is x = h / (f - g).
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