Answer:
17
Step-by-step explanation:
Substitute n = 10 into the n th term rule, that is
a₁₀ = 10 + 7 = 17
The ratio of boys to girls in a group is 5:3. If there are 18 more boys than girls, work out how
many people there are in total.
45 boys, 27 girls
============================================================
Explanation:
g = number of girls
g+18 = number of boys, since there are 18 more boys than girls
For example, if g = 7, then g+18 = 7+18 = 25. In this example, we have 7 girls and 25 boys. The problem with this example is the ratio of boys to girls is 25:7 which is not equal to 5:3
We could use trial and error until we land on the solution, or we can use algebra as shown in the next section.
-------------------
The ratio of boys to girls is 5:3, meaning
(number of boys)/(number of girls) = 5/3
which turns into
(g+18)/g = 5/3
after we make the proper substitutions
Let's solve for g
(g+18)/g = 5/3
3(g+18) = 5g
3g+54 = 5g
54 = 5g-3g
54 = 2g
2g = 54
g = 54/2
g = 27
There are 27 girls.
This leads to,
g+18 = 27+18 = 45
So there are 45 boys
In total, we have 27+45 = 72 people
-----------------------------
Checking the answer:
The claim is that 45/27 is the same as 5/3
For now assume that claim is true. Set the fractions equal to each other and use cross multiplication like so
45/27 = 5/3
45*3 = 27*5
135 = 135
The third equation has the same thing on both sides, so it's a true equation. This must mean the first equation is true as well. Therefore, 45:27 and 5:3 are the same ratio and the answer is confirmed.
You could also use your calculator to note that
45/27 = 1.667
5/3 = 1.667
both decimal values are approximate.
The people there are in total of 72 students
Let the ratio of boys to girls be 5x: 3x
The ratio of boys to girls in a group is 5:3.
What is the formula?
no. of boys = 18 + no. of girls
=> 5x = 18 + 3x
=> 5x - 3x = 18
=> 2x = 18
=> x = 18/2
x= 9
No. of boys = 5x
No. of boys= 5 × 9
No. of boys= 45
No. of girls = 3x
No. of girls= 3 × 9
No. of girls= 27
Total = 45 + 27
Total= 72
Hence, there are 72 students there.
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what is the value of n?
enter answer in box
Answer:
6!
Step-by-step explanation:
chord x chord = chord x chord
(5) (n+8) = (7) (n+4)
i just started plugging in numbers
(5) (6+8) = (7) (6+4)
5 x 14 = 7 x 10
70=70
the area of a rectangular lawn is 255 metre square if its length is 15 M find its perimeter
Answer:
Step-by-step explanation:
width is 255/15=17
perimeter = 17*2+15*2=64
EZ
) Which of the following is the correct equation of a vertical line that contains (5, 6)?
Answer:
[tex]y = {x}^{2} - 11x + 30[/tex]
If anybody answers these questions I will get them brainliest and if somebody else verifies that it is the correct answer I can give you a thanks.
Part (a)
Answer: x^3 + 12x^2 + 47x + 60--------------------------
Work Shown:
Let's say we have
L = length = x+5W = width = x+4H = height = x+3To find the volume of the block, we multiply the length width and height.
So,
volume = (length)*(width)*(height)
V = L*W*H
V = LW*(x+3) .... replace H with (x+3)
V = LW*x + LW*3 .... distribute
V = Lx*(W) + 3L*(W)
V = Lx(x+4) + 3L(x+4) .... replace W with x+4
V = Lx^2 + 4Lx + 3Lx + 12L .... distribute
V = Lx^2 + 7Lx + 12L
V = x^2*(L) + 7x*(L) + 12*(L)
V = x^2*(x+5) + 7x*(x+5) + 12*(x+5) .... replace L with x+5
V = x^3 + 5x^2 + 7x^2 + 35x + 12x + 60 .... distribute
V = x^3 + 12x^2 + 47x + 60
x^3 + 12x^2 + 47x + 60 is the polynomial in standard form that represents the volume of the block.
=======================================================
Part (b)
Answer: 336 cubic feet--------------------------
Work Shown:
We can plug x = 3 into the polynomial we found
V = x^3 + 12x^2 + 47x + 60
V = (3)^3 + 12(3)^2 + 47(3) + 60
V = 27 + 12(9) + 47(3) + 60
V = 27 + 108 + 141 + 60
V = 336
Or we could find the volume like this
V = L*W*H
V = (x+5)*(x+4)*(x+3)
V = (3+5)*(3+4)*(3+3)
V = (8)*(7)*(6)
V = 336
Either way, we get the same volume of 336 cubic feet.
Use the diagram and the information given to find the indicated measure:
1. ZX is the perpendicular axis of WY, yYZ = 13.75. Find the value of WZ.
2. ZX is the perpendicular axis of WY,
WZ = 4n − 13, and YZ = n + 17. Find the value of
AND Z.
3. Find the value of WX when
W Z = 20.5, W Y = 14.8, and Y Z = 20.5
Which expression is equivalent to the expression below?
2(6k+4)−4(2+2k−1)
-------------------------------------------------------------------------
a} 18+48k
b} 14k−1
c} 4k−4
d} 4+4k
Answer:
D. 4+4k
Step-by-step explanation:
(12k +8) - (8+ 8k - 4)
12k +8 - 8 - 8k + 4
4k +4
d}4+4k
2(6k+4)-4(2+2k-1) writing down the question
12k+8-8-8k+4 multiplying the numbers by the coefficients
12k-8k+8-8+4 collecting like terms
4k+4 the answer
Find the value of sin theta, if tan theta = 4; 180 < theta <270.
a. -4 (square root)17/ 17
b. -4
c. -1/4
d. (square root)7/ 4
Please select the best answer from the choices provided
Ο Α
O B
О С
O D
Answer: You can use the identity THE PICTURE THAT I PUT THERE
The sign is negative because the angle is in the 3rd quadrant. This corresponds to ... a. -(4√17)/17
value of sin ( theta ) = -4 (square root of ) 17 / 17
What are Trigonometry Functions ?
Real functions which relate to an angle of a right angled triangle to ratios of two side length.
Given
tan (theta) = 4`
sin(theta) = tan (theta ) / (1 + tan ^ theta)^(1/2)
sin(theta) = 4/(1+(4)^2)^(1/2)
= 4/ (17)^ (1/2)
multiplying and dividing by 17 ^ (1/2), we get
= -4 (17) ^ (1/2) / 17 ( negative since angle is in third quadrant and tan is negative in that quadrant )
option a) -4 (square root of ) 17 / 17
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A circle has a radius of 14 feet. What is the exact area of the circle and what is the approximate area of the circle and What is the appropriate circumference of the circle.
Answer:
Step-by-step explanation:
Exact area of circle = πr² = 196π sq ft
Approximate area of circle = 615 sq ft
Approximate circumference = 2πr = 88 ft
Answer:
615.75ft²
Step-by-step explanation:
A=πr²=π·14²≈615.75ft²
Jane and 3 friends decided to split the cost of a pizza evenly. The total cost was $25.48. How much does each friend have to pay?
Answer:
$6.37
Step-by-step explanation:
Jane and 3 friends = Jane + another 3 people
= 4 people in total
Total Cost of pizza = $25.48
If 4 people split $25.48 evenly,
Amount each friend has to pay = Total Cost of pizza/Total number of people
= $25.48/4
= $6.37 per friend
Each friend has to pay $6.37 each if $25.48 is splitted evenly amongst them
What's the greatest number you can multiply by 8 to get close to, but not go over, 69?
Answer:
8x8=64
happy to help
Step-by-step explanation:
Answer:
you can do 8x8 bc 8x8=64
Step-by-step explanation:
How Many?pls help me.
Answer:
8
Step-by-step explanation:
Help me with this problem please.
Answer:
I believe its 7?
Step-by-step explanation:
sorry if this is wrong
Is
Y=-3/4x -2
Y=3/4x+1
One solution many solution or no solution
Find the area of triangle ABC.
Give your answer correct to 1 decimal place.
А
9 cm
C
10 cm
B
8cm
The area of the triangle ABC is 34.2 square centimeters
How to determine the triangle area?The complete question is in the image
Start by calculating the semi-perimeter using:
s = 0.5 * (a + b + c)
This gives
s = 0.5 * (9 + 10 + 8)
Evaluate
s = 13.5
The area is then calculated as:
[tex]A = \sqrt{s * (s - a) * (s - b) * (s - c)[/tex]
This gives
[tex]A = \sqrt{13.5 * (13.5 - 9) * (13.5 - 10) * (13.5 - 8)[/tex]
Evaluate
A = 34.2
Hence, the area of the triangle ABC is 34.2 square centimeters
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Jamal has 30 ounces of a 20% saline solution. This means 20% of the solution is salt. He combines this solution with 25 ounces of a
30% saline solution
What is the total amount, in ounces, of salt in the combined moxture?
Answer:
13.5 ounces
Step-by-step explanation:
The volume of a cylinder is 63 pi cm^3 . If the radius is 3cm, what is the height of the cylinder?
A. 3.5 cm
B. 21 cm
C. 10.5 cm
D. 7 cm
will give brainliest
Answer:
Step-by-step explanation:
volume = πr²h = π·3²h = 63π
h = 7 cm
The height of the given cylinder is 7 cm. Therefore, option D is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, the volume of a cylinder is 63π cm³ and the radius is 3 cm.
We know that, the formula to find the volume of a cylinder is πr²h.
Now, πr²h=63π
π×3²×h=63π
h= 7 cm
Therefore, option D is the correct answer.
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Help me plssssss!!!!!
Answer:
si yo lo sé tú también cierto
if i have all a's and one d what is my gpa
Answer:
Step-by-step explanation:
umm like 2.8 i think
A group of workers can plant 2/5 acres in days.3/4 What is the unit rate in acres per day?
Answer:
8/15
Step-by-step explanation:
Unit rate is 8 / 15 acres per day.
What is work?
"Work is defined as when force is applied on an object and it gets move in particular direction."
According to the question,
Group of workers plant 2/ 5 acres in 3 /4 days
3 / 4 days = 2/ 5 acres
1 day = [tex]\frac{2}{5}[/tex] × [tex]\frac{4}{3}[/tex]
⇒ 1 day = 8 / 15 acres
Hence, Unit rate is 8 / 15 acres per day.
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James uses 5 1/2 bags of soil to fill 1/4 of his garden. How many bags will James use to fill his entire garden?
Answer:
22 bags
Step-by-step explanation:
Multiply 5 1/2 by 4 and you'll get 22
Answer:
22 bags
Step-by-step explanation:
5 1/2 for 1/4....4/4 for the whole garden. So you can multiply 5 1/2 times 4
Is this not 2? I got 2 and it was wrong
Answer:
Not Proportional
Step-by-step explanation:
Constant of proportionality is what you multiply with x to get y. This is not proportional since its not the same number each time
Answer:
i think its b
Step-by-step explanation:
reason is because 2 divided 2 is not 0 and 6 divided by 2 is not 4
sorry if its wrong ;(
Find the missing side length of this right triangle
10
Tara is playing a party game in which a tiny ball is
dropped into a rectangular box. To win the game, she
must guess where the ball will stop. What should she
guess to maximize her chances of winning?
scribes the likelihood of the ball
quare or rectangular shaped area?
square
circle
triangle
shaded area
4
Answer:
1. Shaded Area 2. UnlikelyStep-by-step explanation:
edge2021
Mark bought a car for x dollars. One year later the car was 0.85x. What was the percent decrease.
Answer:
[tex]Let~the~percentage~decrease~be~equal~to~y.\\Then,\\0.85x = x-\frac{y}{100}(x)\\or, 0.85x = x-0.01xy\\or, 0.85x = x(1-0.01y)\\or, 0.85 = 1-0.01y\\or, 0.01y = 1-0.85 = 0.15\\or, y =15\\So, ~the~decrease~of~the~price~is~15%.[/tex]
Alternative method:
[tex]Percentage~decrease = \frac{Initial~Rate-Final~rate}{Initial~Rate}(100) \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{1-0.85}{1}(100) = 0.15(100)=15[/tex]
Answer:
thr percent decrease is 15%
Step-by-step explanation:
you get 1.00 which represent beginning price u subtract the current price 1.00-0.85 you get0.15 which is 15%
Tell me ASAP plz!! Btw Patsy’s Pasta house uses 3/4 of a cup of sauce for every 12 ounces of pasta...good luck
Answer:
4/6
Step-by-step explanation:
whats a reasonable estimate for 529 divided by 23 ( explain your anwser )
Step-by-step explanation:
First you divide 529 and 23. You can divide 5w9 by 23 in a fraction like this 529/23 on to Desmos scientific calculator or just 529÷23 on a calculator. If it is a decimal, round it up if the tenth, hundredth, or thousandth is 5, 6, 7, 8, 9 or round down if the number is 4, 3, 2, and 1. The answer to 529÷23 is 23. And if you estimate it, it'll be 20. The next part may be a bit confusing but if you estimate 23, you'll get 25.
Then you estimate 529 and 23, you'll get 530 and 20. And if you divide them, you'll get 26.5. And if you estimate that, you'll get 27. So that means is 2 or 7 off from the estimated from the equation 529÷23. So that means the reasonable answer is probably 25 or 27.
Tell me if I'm right or not, and I'm sorry if I'm wrong because I don't know what answer I explained in the two paragraphs I wrote is right or wrong.
Pleaseee help I need this done ASAP will mark brainless if correct!!
I believe its 1/2 because m always stands for slope for slope formula
express in exponential form 200×75
Do you mean exponential form as in scientific notation or as in prime factorization.
Now matter I will do both.
As in scientific notation.
200*75
=150*100
=1.5*10000
=1.5*10^4
As in prime factorization.
200*75
=2^3*5^2*3*5^2
=2^3 * 3 * 5^4
Do the one your teacher ask for :) Hope it helps!
Andy is buying a car.
He negotiated a 7% decrease on a £6 500 car.
He will pay the full balance in 12 equal monthly payments.
Calculate the amount paid each month.
Answer:
£503.75
Step-by-step explanation:
Andy is buying a car.
Step 1
We calculate the decrease
He negotiated a 7% decrease on a £6 500 car.
Decrease = 7% × £6500
= $455
Step 2
We calculate the new price of the car.
= Old price - Decrease
= £6500 - £455
= £6045
Step 3
We calculate the amount he pays every month.
We are told that:
He will pay the full balance in 12 equal monthly payments.
Andy's monthly payments =
New price/12 months
= £6045/12
= £503.75
Therefore, the amount he would be paying each new month = £503.75