Answer:
7-7 = 0
Step-by-step explanation:
Sandy brought different toys from the market, she divided the seven toys into seven children , now she has a total of zero toys left
Total toys left = 7 - 7
Total toys left = 0
Two trees standing side by side in the sunlight one is 50 feet tall and the other is 20 feet tall if the taller tree casts a 18-foot shadow, what is the length in feet of the shadow of the shorter tree
Given:
Length of taller tree = 50 feet
Length of shorter tree = 20 feet
Length of shadow of taller tree = 18 feet
To find:
The length of shadow of shorter tree.
Solution:
Since, two trees standing side by side in the sunlight, therefore the length of trees are proportional to their shadows.
Let the length of shadow of shorter tree be x feet.
Using the given information, we get
[tex]\dfrac{50}{18}=\dfrac{20}{x}[/tex]
By cross multiplication, we get
[tex]50\times x=20\times 18[/tex]
[tex]50x=360[/tex]
[tex]x=\dfrac{360}{50}[/tex]
[tex]x=7.2[/tex]
Therefore, the length of shadow of shorter tree is 7.2 feet.
From house to his job as a janitor, you can walk in a straight line. In the afternoon he has to stop twice on his way home. His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school. The second stop will be at OWL Barbershop for his haircut. The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1. The coordinates of his house are H (-3, -4) and his job coordinates are J(5, 0). Please use B to represent the Bodega and O to represent OWL Barbershop.
Answer:
The coordinates of Bodega is B(1,-2)
The coordinates of OWL Barbershop is O(3,-1)
Step-by-step explanation:
Coordinates of House H = (-3,-4)
Coordinates of Job J= (5,0)
His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school.
Let B to represent the Bodega
Now to find coordinates of Bodega we will use use mid point formula since bodega is exactly halfway between his house and the school.
[tex]x=\frac{x_1+x_2}{2} , y = \frac{y_1+y_2}{2}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\x=\frac{-3+5}{2} , y = \frac{-4+0}{2}\\x=1, y = -2[/tex]
So, The coordinates of Bodega is B(1,-2)
Now we are given that The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1.
Le O to represent OWL Barbershop.
We will use section formula
[tex]x=\frac{mx_2+nx_1}{m+n} , y =\frac{my_2+ny_1}{m+n}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\m:n=3:1\\x=\frac{3(5)+1(-3)}{3+1} , y =\frac{3(0)+1(-4)}{3+1}\\x=3,y=-1[/tex]
So, The coordinates of OWL Barbershop is O(3,-1)
What is the correct order of the numbers from least to greatest. 0, -3/2, 7/3, 2.1, -2
Answer:
-3/2, -2, 0, 2.1, 7/3
Step-by-step explanation:
Please correct me if I am wrong. Thank you.
Can you help me solve this
Step-by-step explanation:
I REALLY NEED HELP IF NOT I'M GOING TO FAIL
Answer:
1. x > 9
2. n < 5
3. b > 2
4. p < 4
5. p < -2
6. m > 0
Step-by-step explanation:
1.
x - 2 - 2 > 5
x - 4 > 5
x > 5 + 4
x > 9
2.
5 + n < 2 x 5
n < 10 - 5
n < 5
3.
50b > 100
b > 100 : 50
b > 2
4.
-5 + p + 2 < 1
p < 1 + 3
p < 4
5.
p + 6 + 8 < 12
p + 14 < 12
p < 12 - 14
p < -2
6.
80m - 64 - 2 > -66
80m > -66 + 66
m > 0:80
m > 0
Of the entering class at a college, % attended public high school, % attended private high school, and % were home schooled. Of those who attended public high school, % made the Dean's list, % of those who attended private high school made the Dean's list, and % of those who were home schooled made the Dean's list. A student is randomly chosen. a) Find the probability that the student made the Dean's list. b) Find the probability that the student , given that the student made the Dean's list. c) Find the probability that the student , given that the student did not make the Dean's list.
Answer:
(a) The probability that the student made the Dean's list is 0.1655.
(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.
Step-by-step explanation:
The complete question is:
Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.
a) Find the probability that the student made the Dean's list.
b) Find the probability that the student came from a private high school, given that the student made the Dean's list.
c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.
Solution:
Denote the events as follows:
A = a student attended public high school
B = a student attended private high school
C = a student was home schooled
D = a student made the Dean's list
The provided information is as follows:
P (A) = 0.71
P (B) = 0.21
P (C) = 0.08
P (D|A) = 0.16
P (D|B) = 0.19
P (D|C) = 0.15
(a)
The law of total probability states that:
[tex]P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})[/tex]
Compute the probability that the student made the Dean's list as follows:
[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)[/tex]
[tex]=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655[/tex]
Thus, the probability that the student made the Dean's list is 0.1655.
(b)
Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:
[tex]P(B|D)=\frac{P(D|B)P(B)}{P(D)}[/tex]
[tex]=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411[/tex]
Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c)
Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:
[tex]P(C^{c}|D^{c})=1-P(C|D^{c})[/tex]
[tex]=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185[/tex]
Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.
Solve by Elimination:
4x + 8y = 20
-4x + 2y = 10
(-1,3)
(3,4)
(3,-1)
(4,3)
Answer:
(-1,3)
Step-by-step explanation:
Elimination makes solving for the system of equations much easier if it is the faster route. In this case, it is already done for you, and no multiplication is required.
First, we want to eliminate the x values completely because they are opposites and therefore cancel out. Next, you want to add the y-values and sum (20 and 10) so that you get the new equation [tex]10y=30[/tex]. To isolate you need to divide by 10 on each side which will give you [tex]y=3[/tex].
Now that you have your y-value, you can plug in your value to either of the equations and find what x is. I will use the equation 4x + 8y = 20 to solve for x. We first want to substitute in our y-value so that we get [tex]4x+8(3)=20[/tex] which is simplified to [tex]4x+24=20[/tex] now subtract by 24 on both sides to get 4x by itself to get [tex]4x=-4[/tex]. Lastly, isolate x by dividing by 4 on each side to get [tex]x=-1[/tex]
xanthe ran one quarter of a kilometer. She took a 5 minute rets, then ran another ten eighths of a kilometer. How many kilometers did she run in total.
Answer:
1 1/2 kilometers
Step-by-step explanation:
She ran 1/4 of a kilometer and then ran another 10/8 kilometer.
The 5 minute rest is to throw people off, so ignore it.
10/8 can simplify to 5/4 kilometers, so you can add that to the first quarter of a kilometer she already traveled.
5/4 plus 1/4 equals 6/4.
6/4 can be simplified to 3/2 which is equal to one and one half.
1 1/2
Hope this helps!
In training for a swim meet, Logan swam 750 meters in \large \frac {1}{3}
3
1
of an hour. His swimming partner, Mila, swam \frac {2}{3}
3
2
of Logan's distance in \frac {1}{4}
4
1
of an hour. 2. What is Mila's average swimming speed? Show your work.
Answer:
500
Step-by-step explanation:
Please find angle q. Thank you!
the angle you are looking for is 9
Which of the following equations represents the total cost, C, for the number of sandwiches, S, where each sandwich costs $7?
1) S = 7C
2)C = 7S
3) S = 7/C
4) C= 7/S
On Monday, Allison’s bank account showed $0. She made 5 transactions that were all the same amount between Monday and Friday. If her bank account showed -$120 on Friday, what was the amount of each transaction?
Answer: $24
Step-by-step explanation: if you divide $120 by 5 then you get $24
if the school is havinng a pizza party they have 6,847 each kid will have 3 slices of the pizza how many slices of pizza the school need to order so each kid can have 3 slices help pls i got class at 8:30
A. The parents of a baby wish to establish a college fund for their child. They deposit
$100 every month into an account for 18 years. The money earns 6 3/8% interest
compounded monthly. Find the future value of this account.
Answer:
FV= $38,735.32
Step-by-step explanation:
Giving the following information:
Monthly deposit= $100
Number of periods= 18*12= 216 months
The interest rate is confusing. I will assume an interest rate of 6%. If it is not correct, just change it in the formula.
Monthly interest rate= 0.06/12= 0.005
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {100*[(1.005^216) - 1]} / 0.005
FV= $38,735.32
Which interval notation represents the set of all numbers greater than 0 and less than or equal to 3?
Answer:
(0,3)
Step-by-step explanation [0,3] indicates that the numbers are greater or equals to 0 and less than or equals to 3; while (0,3) leaves out the equal sign
What is the solution to the system of equations?
6x – 9y = 16
2x – 3y = 7
A) (5, 1)
B) (2, -1)
C) (3,
2
9
)
D) no solution
Answer:
no solution
Step-by-step explanation:
[1] 6x - 9y = 16
[2] 2x - 3y = 7
// Solve equation [2] for the variable x
[2] 2x = 3y + 7
[2] x = 3y/2 + 7/2
// Plug this in for variable x in equation [1]
[1] 6•(3y/2+7/2) - 9y = 16
[1] 0 = -5 => NO solution
No solution
How to Solve this??! 6x-2=x+13
Answer:
x=3
Step-by-step explanation:
We are given the equation, 6x-2=x+13.
1. 6x=x+15
2. 5x=15
3. x=3
Hope this helps! Good luck on your assignment!
Answer: x=3
Step-by-step explanation:
6x-2=x+13
First get both x’s on one side
We are going to subtract x from both sides
5x-2=13
Now we want to get 5x alone
We are going to add 2 to both sides
5x=15
Now we want to get x alone
We are going to divide by 5
x=3
3. A savings account is started with an initial deposit of $3000. The account earns 9% interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach 1 million. Show your work.
Note: 1 million is a 1 with 6 zeros. Note2: you must use log functions to solve.
Answer:
See below
Step-by-step explanation:
GivenDeposit = $3000Interest rate = 9% compoundedNumber of years = tNumber of compounds = 1 per year Solution(a) the equation
f(t) = 3000*(1.09)^t(b) If f(t) = 1000000
1000000 = 3000*(1.09)^t(1.09)^t = 1000000/3000(1.09)^t = 333.3333log (1.09)^t = log 333.3333t log 1.09 = 2.52290.03742t = 2.5229t = 2.5229/0.03742t = 67.4 ≈ 68 years
A photographer reduces the size of a photo by 20%. If the length of each side is 12 cm,
what is the length of the side of the new photo?
Answer:
9.6 cm
Step-by-step explanation:
12 x .8 = 9.6cm
If LN = 6x - 5, LM = x + 7, and MN = 3x + 20, find MN.
A.68
B.16
C.23
D.18
Answer : The correct option is (A) 68.
Step-by-step explanation :
As we are given that:
LN = 6x - 5
LM = x + 7
MN = 3x + 20
Now we have to determine the value of MN.
According to the question:
LN = LM + MN
Now putting all the given values in this expression, we get:
6x - 5 = (x + 7) + (3x + 20)
6x - 5 = 4x + 27
6x - 4x = 27 + 5
2x = 32
x = 16
The value of MN = 3x + 20 = 3(16) + 20 = 48 + 20 = 68
Therefore, the value of MN is 68.
What is the equation of the line that passes through the point (-8,5) and has a slope
of o?
Answer: y = 5
Step-by-step explanation:
If the slope is 0, the graph of the line is a horizontal line (parallel to the x-axis). 0 slope means it is flat.
Here it passes through the y-axis at +5 and passes through every value of x.
Consider the enlargement of the parallelogram. A smaller parallelogram with side lengths of one-third foot and x feet. A larger parallelogram with side lengths 8 feet and 6 feet. Set up a proportion to solve for the missing measure of the original parallelogram. Which side of the original parallelogram corresponds to the 6 ft side of the enlarged parallelogram? What is the second step in solving the proportion? What is the value of the missing measure?
Answer:
Enlargement rate is 24
Step-by-step explanation:
Divide 8 by one third to get the enlargement rate. I hope this helps:)
Answer:
Which side of the original parallelogram corresponds to the 6 ft side of the enlarged parallelogram? ITS IS x ft
What is the second step in solving the proportion? IT IS cross multiply
What is the value of the missing measure? IT IS 1/4
Step-by-step explanation:
i got this right
calculate and interpret the residual for the high school senior with foot length of 20 cm and a height of 160 cm
Answer:
try quizlet it would help:)))
Answer:
Step-by-step explanation:
The vertical distance between a senior student with a height of 160 cm and his estimated height of 157.06 cm is 2.94 cm
select the answers below that are equivalent to 18/30
A.15/25
B.6/11
C.3/4
D.3/5
E. 9/15
Answer:
A, D ,E
Step-by-step explanation:
18/30
Divide the top and bottom by 6
3/5
A.15/25 Divide top and bottom by 5 = 3/5
B.6/11 cannot be simplified
C.3/4 cannot be simplified
D.3/5 cannot be simplified
E. 9/15 divide top and bottom by 3 = 3/5
I need help with this and explain how to do it please!!
6x - 4z
Answer:
you should know you dont need help so do it by yourself. if you want the awnser you should know or you just dont pay attention in class.1234567890 is your awnser
what is the justification for Step 1 in the solution process?
Answer:
mulitply
Step-by-step explanation:
PEMDAS
mutiply
divide
add
and subtract
What do you know about distance? math
Answer: Mathematical distance is defined as the amount of space between two points. This distance can be calculated using the distance formula, which is just a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the other two sides
Step-by-step explanation:
Find the reciprocal: 5/6
A. 1/6
B. 1/5
C. 5/6
D. 6/5
Answer:
D
Step-by-step explanation:
just flip the fraction
Answer:
D
Step-by-step explanation:
The reciprocal is just the fraction flipped.
CAN SOMEONE HELP ME PLZ THIS WAS DUE LIKE 5 minutes ago!!
Answer:
-4[tex]x^{2}[/tex] - 6
Step-by-step explanation:
First you have to add the two polynomials. Write the first equation then line up the second equation below the first making sure to keep the columns correct. [tex]x^{2}[/tex] goes in one column, x goes in the next column and the whole numbers go in the last column. Also be sure to have the correct signs of those columns. It should look like this:
4[tex]x^{2}[/tex] - x + 1
PLUS -6[tex]x^{2}[/tex] + x - 4
-----------------------
-2[tex]x^{2}[/tex] + 0 - 3
Note that the middle x turns to 0 because you're subtracting 1x from 1x which is 0.
You can now write the SUM as -2[tex]x^{2}[/tex] - 3
Now they want to know what twice this sum is so multiply it by 2
2 ( -2[tex]x^{2}[/tex] - 3) = -4[tex]x^{2}[/tex] - 6
Simplify the expression.
3p – 49 + 9 = 8p
Answer:
p=-5
Step-by-step explanation:
3p-49+9 -49+9=-40
3p-40=8p 3p-3p=0 8p-3p=5p
-40=5p p=5