Answer:
here are 3 times as many boys as girls in a room. If 4 boys and four girls leave the room, then there will be 5 times as many boys as girls in the room. In total, how many boys and girls were in the room originally?
8 girls
24 boys
There were 24 boys and 8 girls in the room originally.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Given that there are 3 times as many boys as girls in a room.
If 4 boys and 4 girls leave the room, then there will be 5 times as many boys as girls in the room.
Let's assume the number of boys would be b
And the number of girls would be g
According to the given condition, the required solution would be as:
b = 3g ....(i)
b - 4 = 5 (g - 4) ....(ii)
Substitute the value of b = 3g in equation (ii), and solve for g
3g - 4 = 5 (g - 4)
3g - 4 = 5g - 20
5g - 3g = 20 - 4
2g = 16
g = 8
Substitute the value of g = 8 in equation (i), and solve for b
b = 3 × 8
b = 24
Hence, there are 24 boys and 8 girls in the room.
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Shawn has two investments which both are compounded annually. Investment x earns 5% interest, and investment y earns 7% interest. Each year Shawn has to pay an 18% tax on the net gain of her investments to the IRS. Which equation can Shawn use to determine the amount of money, t, she will need to pay the IRS?
Answer:
0.18(0.05x + 0.07y) = t
explanation:
Trust me
a moving company charges $0.40 per pound. a family estimates that their belongings weight 3 tons. about how much would it cost the family to move their belongings?
Answer:
$2,400
Step-by-step explanation:
3 tons equals 6000 pounds
6000*0.40= $2,400
2 more because im going broke lol
Bob and chris share some money in the ratio 2:3.
Bob receives £8
Work ouy how much Chris receives.
Answer:
Chris will receive 4 euros
Answer:
12
Step-by-step explanation:
Use synthetic division to evaluate f (x)= x^3+ 6x^2-2x - 12 when x = 3
The function value of given function at x = 3 is 63.
Synthetic division :The given function is,
[tex]f(x)=x^{3} +6x^{2} -2x-12[/tex]
We have to calculate function value when [tex]x=3[/tex].
[tex]f(3)=3^{3} +6*3^{2}-2(3)-12\\ \\f(3)=27+54-6-12\\\\f(3)=81-18\\\\f(3)=63[/tex]
Thus, the function value of given function at x = 3 is 63.
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Eugene ate 20% of the Christmas cookies his
grandmother made. If he ate 8 cookies, how
many are left?
Answer:
40 is the total amount of cookies
32 is the amount left
Step-by-step explanation:
If 20% of cookies equal to 8 then to find how many are there in total we multiply 8 with 100 then divide it with 20
8 × 100 ÷ 20 = 40
find the slope given the points (1,4) and (5,9)
Answer:
the slope is 5/4
Step-by-step explanation:
use the formula y2 - y1 over x2 - x1, and plug in the coordinates into that
The slope of the line whose points are (1, 4) and (5, 9) will be 1.25.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given below.
(1, 4) and (5, 9)
The slope of the line is given as,
m = (9 - 4) / (5 - 1)
m = 5/4
m = 1.25
The slope of the line whose points are (1, 4) and (5, 9) will be 1.25.
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A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 238 graduating seniors and found the mean score to be 493 with a standard deviation of 97. Calculate the margin of error using the given formula. How could the results of the survey be made more accurate?
Answer:
±12.323
Step-by-step explanation:
A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of 238 graduating seniors and found the mean score to be 493 with a standard deviation of 97. Calculate the margin of error using the given formula. How could the results of the survey be made more accurate?
The formula for margin of Error =
±z × Standard deviation/√n
We are not given the confidence interval but let us assume the confidence interval = 95%
Hence:
z score for 95% confidence interval = 1.96
Standard deviation = 97
n = random number of samples = 238
Margin of Error = ± 1.96 × 97/√238
Margin of Error = ±12.323
The margin of error using the given formula will be ±12.323.
What is the error?An error is a mistaken or erroneous action. In some contexts, an error is interchangeable with a mistake.
The discrepancy between the calculated value and the correct value is referred to as an "error" in statistics.
Given data;
Confidence interval = 95%
z score for 95% confidence interval = 1.96
Standard deviation = 97
n is a random number of samples = 238
The margin of Error is found as;
E =±z × Standard deviation/√n
[tex]\rm E= +z \times \frac{\sigma}{\sqrt{n} }[/tex]
[tex]\rm E=\±1.96 \times \frac{97}{\sqrt{238} }\\\\ E=\±12.323 \[/tex]
Hence,the margin of error using the given formula will be ±12.323.
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How many years will it take an investment to double at 6.4% compounded monthly? (Round to the nearest tenth))
Answer:
Number of Years to Double= 10.62 years
Step-by-step explanation:
First, we need to calculate the real annual interest rate:
Real annual interest rate= {[(i/12)+1]^12} - 1
Real annual interest rate= [{(0.064/12) + 1]^12 - 1}
Real annual interest rate= 0.0659
Now, we need to use the rule of 72. The rule of 72 is a means of estimating the number of years it takes for an investment or your money to double.
Number of Years to Double= 70/Annual Rate of Return
Number of Years to Double= 70/6.59
Number of Years to Double= 10.62 years
George borrowed $25,000 for a new car. If George pays simple interest at a rate of
4/12% for 4 years, how much interest will he pay?
Answer:
To answer your question use the code ICE on here to get your answer works every time for me hope this helps
Answer:
$93,585.53
Step-by-step explanation:
If he is paying interest continually, you would use the formula Pe^rt
25000e^.33(4)= 3,585.53
If he used any other type of interest (monthly=12, quarterly=6, semi-annually=2, or annually=1) then you would use the formula p(1+r/n)^nt
25000(1+.33/n)^n(4)
n= put the number for how much you pay interest
Runners who achieved a time between 37 and 48 minutes to complete the race were each awarded a silver medal. (c) Calculate an estimate of the number or runners awarded silver medals
Answer:
The data is missing, However the answer is given below
Step-by-step explanation:
The data is missing about the runners and the duration minutes taken to complete the race, However the answer is given below
(3 * 4) + (8 * 3)
12 + 24
36 silver medals would have been awarded to runners.
The data is missing for the runners of the race and the time they took to complete the race, silver medal is awarded for runners who completed race in 37 to 38 minutes.
Which expression is equivalent to 7a -8-12a+4?
A) -9a
B) 31a
C) -5a - 4
D) 19a + 12
According to the ratio of the age, if Rs. 216 is divided to the girls of age 8, 9 ad 10 yearsHow much money will each get
9514 1404 393
Answer:
8 years: Rs. 649 years: Rs. 7210 years: Rs. 80Step-by-step explanation:
The sum of ages is 8+9+10 = 27, so each year of age is rewarded by ...
216/27 = 8 . . . Rs
Then age 8 gets 8(Rs. 8) = Rs. 64
age 9 gets 9(Rs. 8) = Rs. 72
age 10 gets 10(Rs. 8) = Rs. 80
The total price of five DVDs (all the same cost) and four movie tickets (all the same cost) is $138, whereas, the total price of two DVDs and five movie tickets is $96. What is the price of one movie ticket? Answer as a number with NO units and NO decimals. Only give the answer to the question asked.
Answer:
Step-by-step explanation:
Let the price of DVDS = x
The price of movie tickets = y
The total price of five DVDs (all the same cost) and four movie tickets (all the same cost) is $138,
= 5x + 4y = $138
The total price of two DVDs and five movie tickets is $96.
2x + 5y = $96
Hence:
5x + 4y = $138.... Equation 1
2x + 5y = $96..... Equation 2
What is the price of one movie ticket?
Elimination method
2y = 204
y = 204/2
y = 102
What is the perimeter of the triangle formed by (-3,1),(-3,5), and (4,1)
Answer:
15
Step-by-step explanation:
Have a nice Day , Hope this helped you I would appreciate it if you could mark my answer brainliest
Solve the following proportion for n.
4/12 = n/72
Answer:
n = 24
Step-by-step explanation:
(4/12)*72 = n
24 = n
Please help due in 10 min
PLEASEEEEE HELPPPP!
Answer:
option 4
Step-by-step explanation:
put like terms on either side
9x + 2a = 3a - 4x
subtract both sides by 2a
9x = a - 4x
add both sides by 4x
13x = a
divide both sides by 13
x = a/13
please give thanks, hit that heart button :)
Answer:
4.) a/13
Step-by-step explanation:
9x + 2a = 3a - 4x
9x + 4x = 3a - 2a
13x = a
13x/13 = a/13
x = a/13
z = y + x + m , solve for x
step by step
in this in this equation y equals 14 x what is the constant of proportionality
Answer:
We conclude that the value of the constant of proportionality.
k = 14Step-by-step explanation:
We know that if 'y' varies directly with 'x', we use the equation
y ∝ x
y = kx
where 'k' is called the constant of proportionality.
Given the equation
y = 14x
comparing with the equation
y = kx
Thus,
k = 14
Therefore, we conclude that the value of the constant of proportionality.
k = 14Which is a counterexample of the following conjecture: "If two angles are supplementary, they have the same measure?"
A:30 degrees and 60 degrees
B:50 degrees and 130 degrees
C:90 degrees and 90 degrees
D:45 degrees and 45 degrees
Answer:i dont know but i think its D.
Step-by-step explanation:
Pls mark meh Brainlessed
My friend justen here hes tacken and hes cracked at fornight my guy AHHHH A BREAD DOG
What are the coordinates of the center and the
length of the radius of the circle whose equation is
(x + 1)² + (y – 5) = 16?
1) (1,-5) and 16
2) (-1,5) and 16
3) (1,-5) and 4
4) (-1,5) and 4
Answer:
I think 3 not sure don't angry if wrong
The expression 15 n + 5 n + 5 Which is another way to write this expression?
Answer:
cbdkkdfn
Step-by-step explanation:
bfnsowifnccvl
Answer:
Ok
Step-by-step explanation:
(15n+5n)+5
Which fraction is not equivalent to 7/8?
A. 21/24
B. 35/40
C. 15/16
D. 28/32
Hlep pls
Answer:
15/16
Step-by-step explanation:Because - 7×2=14×
8×2=16=16✓
A large bottle of juice contains 500 milliliters of juice. A medium bottle contains 70% as much juice as the large bottle. How many milliliters is 25% of the large bottle?
Answer:
The other answer is wrong
Step-by-step explanation:
Because it said that on my test...
If JK = KL, find JL Please help me.
Answer:
JL=22x-6
Step-by-step explanation:
We have JK=KL
Si multiplicas 2 números enteros que no tienen el mismo signo, ¿el resultado será un número entero positivo o uno negativo?
resposta:
Número entero negativo
explicación paso a paso:
Para ilustrar esto, elegimos dos números enteros con diferentes signos: 5 y -6
Si los multiplicamos:
[tex]5x-6=-30[/tex]
El resultado siempre será un número negativo con diferentes signos: 5 y -6
por favor márcame como el brainliest
what is the solution (x,y) to the system of equations? x=10 3x+5y=20
Answer:
(10, -2)
Step-by-step explanation:
x = 10 (its given in the problem)
then plug in 10 for x in the second equation and solve for y
3(10) + 5y = 20
30 + 5y = 20
5y = -10
y = -2
so the solution is (10, -2)
PLEASEEEE HELPPP!!!!
Answer:
A.
Step-by-step explanation:
Can you find the slope and type the correct code?
Answer:
number 4 : m= -2
Step-by-step explanation