As per linear equation, there are 372 more girls in school than boys.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant."
Given, there are 1970 pupils.
There are 799 boys in the school.
Therefore, the number of girls in the school is
[tex]= (1970-799)\\= 1171[/tex]
Therefore, the number of girls more than boys in the school is
[tex]= (1171-799)\\= 372[/tex]
In that school , there are 372 more girls than total number of the boys.
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Write the expression t = 8 + 2h to represent the
temperature change for that day. Circle all of the expressions below that are equivalent to T
t=8+2h
a. t = h + 8 + 2h
c. t = 4h + 6 - 2h + 2
b. t= 8 + h + h
d. t = 8 - 2h
how to find the hcf and the lcm of numbers using prime factorization.
lcm
30 and 12.
hcm
12 and 20
Answer:
Below in bold.
Step-by-step explanation:
30 = 2 * 3 * 5
12 = 2 * 2 * 3
Note that 2 and 3 are common to both factors
so the HCF = 2*3 = 6.
Only one 2 and one 3 of the duplicates are included in the LCM:
so the LCM = 2 * 3 * 2 * 5 = 60
20 = 2 * 2 * 5
12 = 2 * 2 * 3
HCF = 2 *2 = 4
LCM = 2*2*3*5 = 60.
A chocolatier is creating chocolate truffles in the shape spheres. The truffles will be solid chocolate and have a radius of 2.5 cm. How much should each truffle weigh if chocolate weighs 0.71 grams per cubic centimeter? (round to the nearest tenth, if necessary)
The truffles will have a volume of [Answer] cubic centimeters and will weigh a total of [Answer] grams.
Answer: Volume: 65.4 Weight: 46.4
Step-by-step explanation:
Density describes mass per unit volume. The weight of each of the considered chocolate truffle is 46.47 grams approx.
What is density?Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.
Density = (Total amount available)/(total space which contains that amount)
We're given that:
The chocolate weighs 0.71 grams per cubic centimeter. This is density of the considered chocolate, as it is telling that 0.71 grams of chocolate is available per cubic cm.The chocolate truffles are in shape of sphere with radius 2.5 cmVolume of each chocolate truffle = volume of sphere with radius 2.5 cm
= [tex]\dfrac{4}{3} \pi (2.5)^3 \approx 65.45 \: \rm cm^3[/tex]
One cubic cm has 0.71 grams weight,
so one truffle, which has 65.45 cubic cm of chocolate, will weigh approx[tex]0.71 \times 65.45 \approx 46.47 \: \rm g[/tex]
Thus, the weight of each of the considered chocolate truffle is 46.47 grams approx.
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The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount. The half-life of the radioactive gas radon is approximately 2.8 days. The initial amount of radon used in an experiment is 74 grams. If N represents the number of grams of radon remaining t days after the start of the experiment,
a. Write an equation that gives Nin terms of t.
b. how much gas radon approximately remains after 2.8 days?
c. approximately when will the amount of radon remaining be 10 grams?
Step-by-step walkthrough:
a.
Well a standard half-life equation looks like this.
[tex]N = N_0 * (\frac{1}{2})^{t/p[/tex]
[tex]N_0[/tex] is the starting amount of parent element.
[tex]N[/tex] is the end amount of parent element
[tex]t[/tex] is the time elapsed
[tex]p[/tex] is a half-life decay period
We know that the starting amount is 74g, and the period for a half-life is 2.8 days.
Therefore you can create a function based off of the original equation, just sub in the values you already know.
[tex]N(t) = 74g * (\frac{1}{2})^{t/2.8days[/tex]
b.
This is easy now that we have already made the function. Here we just reuse it, but plug in 2.8 days.
[tex]N(t) = 74g * (\frac{1}{2})^{t/2.8days} = N(2.8days) = 74g * (\frac{1}{2})^{2.8days/2.8days}\\= 74g * \frac{1}{2} = 37g[/tex]
c.
Now we just gotta do some algebra. Use the original function but this time, replace [tex]N(t)[/tex] with 10g and solve algebraically.
[tex]10g = 74g * (\frac{1}{2})^{t/2.8days}\\\\\frac{10g}{74g} = (\frac{1}{2})^{t/2.8days}[/tex]
Take the log of both sides.
[tex]log(\frac{5}{37}) = log((\frac{1}{2})^{t/2.8days})[/tex]
Use the exponent rule for log laws that, [tex]log(b^x) = x*log(b)[/tex]
[tex]log(\frac{5}{37}) = \frac{t}{2.8days} * log(\frac{1}{2})[/tex]
[tex]\frac{log(\frac{5}{37})}{log(\frac{1}{2})} = \frac{t}{2.8days}[/tex]
[tex]2.8 * \frac{log(\frac{5}{37})}{log(\frac{1}{2})} = t[/tex]
slap that in your calculator and you get
[tex]t = 8.1 days[/tex]
Solve Systems of Equations Using the Substitution Method
6x - y= -4
2x + 2y = 15
I genuinely do not understand this concept at all, it would be AMAZING, if you could explain this as well.
Thanks, all.
Answer:
x= ½, y= 7
Step-by-step explanation:
[tex]\textcolor{steelblue}{\text{\textcircled{1} Label the equations}}[/tex]
6x -y= -4 -----(1)
2x +2y= 15 -----(2)
[tex]\textcolor{steelblue}{\text{\textcircled{2} Make y the subject of formula}}[/tex]
We could also make x the subject of formula in one equation, however the equation can be easily rearranged so that the coefficient of y is 1. This can be done by moving the y term to the right hand side of the equation, and the rest to the left. Note that each time you bring a term or constant over to the other side of the equation, its sign changes (e.g. positive to negative).
From (1):
6x +4= y
y= 6x +4 -----(3)
Label the equation as equation (3) so we can refer to it easily later.
[tex]\textcolor{steelblue}{\text{\textcircled{3} Substitute (3) into (2)}}[/tex]
Now that we have an equation of y that is written in terms of x, we can replace all the y in equation (2) so that the whole equation is only in terms of x.
Subst. (3) into (2):
2x +2(6x +4)= 15
Expand:
2x +12x +8= 15
Simplify:
14x +8= 15
14x= 15 -8
14x= 7
x= 7 ÷14
x= ½
[tex]\textcolor{steelblue}{\text{\textcircled{4} Find y}}[/tex]
Substitute x= ½ into (3):
y= 6(½) +4
y= 3 +4
y= 7
Ashton is solving the equation
3x + 7 = 16.
Which shows a step Ashton can
use to solve the equation?
a. 3x + 7 = 16 - 7
b. 3x + 7 - 7 = 16 - 7
c. 3x + 7 = 16 + 7
d. 3x + 7 + 7 = 16 + 7
PLEASE HELP
Answer:
B: 3x + 7 - 7 = 16 - 7
Step-by-step explanation:
B: 3x + 7 - 7 = 16 - 7
Answer:
[tex]\boxed{\sf{B. \quad3x + 7 - 7 = 16 - 7}}[/tex]
[tex]\boxed{\sf{x=3}}[/tex]
Step-by-step explanation:
Isolate the term of x from one side of the equation.
3x+7=16First, subtract by 7 from both sides.
⇒ 3x+7-7=16-7
Solve.
⇒ 16-7=9
Rewrite the problem down.
⇒ 3x=9
Divide by 3 from both sides.
⇒ 3x/3=9/3
Solve.
Divide the numbers from left to right.
⇒ 9/3=3
⇒ x=3
Therefore, the solution is x=3, which is our answer.So, the correct answer is B. 3x+7-7=16-7 (second option).I hope this helps you! Let me know if my answer is wrong or not.
Copare use <,>, or =
Answer:
0.125 = ⅛
Step-by-step explanation:
Both are equal.......
75% of 1250
find the value
Answer:
937.5
Step-by-step explanation:
Given:
75% of 1250
Note:
Of = Multiply
Solve:
75% × 1250
= 937.5
~Lenvy~
Answer:
937.5
Step-by-step explanation:
We Know That 75% Is Same As 75
100
So, You Start By Dividing That, Or Making The Calculation Together, You Say
[tex] \frac{75}{100} \times \frac{1250}1[/tex]
[tex]0.75 \times 1250[/tex]
[tex] = 937.5[/tex]
helppppppppp meee too simplify this
Answer:
30,976
Step-by-step explanation:
=}.
[tex](11 {}^{3} \times 4 { }^{2} \binom{}{11 {}^{2} } ) {}^{2} [/tex]
=}.
[tex](11 \times 4 {}^{2} ) {}^{2} [/tex]
=}.
[tex]121 \times (4 {}^{2} ) {}^{2} [/tex]
=}.
[tex]121 \times 256[/tex]
=}. 30,976
Answer:
Answer given above
Step-by-step explanation:
11^2 * 4^4
Julia was creating similar triangles in the coordinate plane. The first triangle had a rise of 3 and a run of 10. The second triangle had a rise of 7. 5. Analyze Julia’s work to see if she found the correct length of the run for the second triangle to be similar to the first triangle. 1. 3 10 = 7. 5 x 2. 75 = 3x 3. X = 25 Is Julia correct? If not, what was her mistake? Yes, she is correct. No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios. No, she needed to have the product of the numerators equal to the product of the denominators. No, she needed to multiply 7. 5 to both sides.
Yes julia is correct the run of the scond similar triangle will be b2=25.
What are simlilar traingles?The similar triangle are those whose three sides or one angle or two sides or two angles one side are equal.
In the given:
Height of first triangle h=3
Base of first traingle =10
Height of second triangle =7.5
The base of second triangle b2 = ?
From the triangle similarity
[tex]\dfrac{h_1}{b_1}=\dfrac{h_2}{b_2}[/tex]
[tex]\dfrac{3}{10}=\dfrac{7.5}{b_2}[/tex]
[tex]b_2=\dfrac{7.5\times 10}{3}[/tex]
[tex]b_2=25[/tex]
Thus julia is correct the run of the scond similar triangle will be b2=25.
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Tickets at a particular movie theater have different rates for adults and children. On Tuesday the theater sold 4 adult tickets and 9 child tickets for $88. The next day, the theater sold 7 adult tickets and 5 children tickets for $111. What is the price for the adult ticket and the price for the child ticket?
Answer:
Adult Ticket = $13.00, Children Ticket = $4.00
Step-by-step explanation:
13*4=52, 4*9=36, 52+36=88
13*7=91, 4*5=20, 91+20=111
Find the measure of the missing angle
The two angles form a straight line and need to equal 180 degrees
180 - 61 = 119
The missing angle is 119 degrees
Which of the following situations results in 2/3 ? Select three that apply
Answer:
The first, second, and fourth questions.
Step-by-step explanation:
None of these result in an answer of 23, so I'm assuming that you meant 2/3.
"Two gallons of water are needed to fill 3 fish tanks of equal size. How many gallons of water are required for each tank?"
2 gallons divided between 3 tanks is 2 divided by 3, so 2/3.
"Three cats share 2 cans of tuna. How much of a can does each cat receive?"
2 cans divided between 3 cats - it's the same as the above problem, just with cats and tuna cans instead of tanks and gallons of water. Each cat gets 2/3 of a can.
"Two bags of bird seed are split among 5 parrots. What fraction of a bag does each parrot receive?"
2 bags divided between 5 parrots would be 2/5 of a bag for each parrot.
"Two apples are split among 3 people. How much of an apple does each person receive?"
Two apples split among 3 people - like the first 2 questions, this also equals 2/3.
"Three dogs each drink 2 cups of water. How many cups of water do the dogs drink in all?"
Three dogs EACH drink 2 cups of water means that the answer is 2*3=6 cups.
"Three cupcakes are divided among 2 children. How much of a cupcake does each child receive?"
Three cupcakes are split between 2 children - they will each get 3/2 of a cupcake, or 1 1/2.
There are 6 orange marbles, 2 red marbles, 3 white marbles, and 4 green marbles in a bag. Once a marble is drawn, it IS replaced. Find the probability of selecting 2 orange marbles in a row P(orange, orange). Write your answer as a simplified fraction
The probability of selecting two orange marbles with replacement is 36/169.
Data;
Orange= 6Red = 2Green = 4Probability with replacementSince after each draw, the orange marble is replaced.
The total number of marbles in the bag is
6+3+4 = 13
And the number of orange marbles is 6.
For the first selection, the probability of selecting one orange is
[tex]P = \frac{6}{13}[/tex]
After drawn and replaced, the probability of selecting another marble is
[tex]P = \frac{6}{13}[/tex]
And the probability of selecting two orange marbles with replacement is
[tex]P = \frac{6}{13} * \frac{6}{13} = \frac{36}{169}[/tex]
The probability of selecting two orange marbles with replacement is 36/169.
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If 2 fair dice are tossed what is the probability that the sum of the number of dots on the top faces will be 7
Answer:
⅙
Step-by-step explanation:
it could be 6 and 1, 5 and 2, 4 and 3, 3 and 4, 2 and 5 or 1 and 6.
It is 2 fair dice, so all together, the probability is 36.
6/36 can be simplified to ⅙
marks obtained by the students are 12,16,14,13,19 and x . If their average marks is 15. find the value of x.
step by step
process by process
needed answer
making them as a brainlists
Answer:
x = 16
Step-by-step explanation:
Given:
Number of students = 6Average mark = 15Therefore, total marks = 15 × 6 = 90
To find the value of x, add up the individual marks:
12 + 16 + 14 + 13 + 19 + x = 74 + x
Now equate this to the total number of marks found previously:
74 + x = 90
Solve for x:
⇒ 74 + x - 74 = 90 - 74
⇒ x = 16
Therefore, the value of x is 16.
The graph below represents the result of a survey in which a number of students
reported how many letters were in their last names.
How many students have a name that's longer than 8
letters?
Answer:
2
Step-by-step explanation:
One we student has 9 letters and another has 10 letters
find the HCF of
[tex]5x {}^{2} - 125,x {}^{2} + 25and - 10x[/tex]
Answer:
Step-by-step explanation:
5x^2 - 125 factors into 5 (x^2 - 25)
x^2 - 25 factors into (x + 5)(x - 5)
So the answer to this part is 5(x + 5)(x - 5)
x^2 - 10x + 25 factors into
(x - 5)(x - 5)
So the HCF is (x - 5)
Find the value of x for which ABCD must be a parallelogram.
Which quadratic function in vertex form can be represented by the graph that has a vertex at negative 4. . 5. and passes through the point negative 7. . 11. ?
Answer:
the annswer is 4155 because its in formal information
Step-by-step explanation:
the annswer is 4155 because its in formal information
Estimate the difference.
Answer:
498. 498/6 = 83.
Step-by-step explanation:
Select all the statements that describe the distribution of the data
Which number sentence matches the question below?
Mindy has a total of 239 books.
If Mindy gives 92 books to her local library, how many books will she have left?
A.
- 239 = 92
B.
239 + 92 =
C.
239 - 92 =
Answer:
Your answer is C.
239-92
Step-by-step explanation:
If shes giving AWAY then it would be a subtraction problem.
Which table does NOT represent a linear function?
Hey there!
Linear functions have a continuous change.
Let's check these tables and see if we can tell linear functions from non-linear functions.
The first one is
x values: -1, 0, 1, 2- we add 1 each time
y values: 8, 5, 2, -1- we subtract 3 each time
[tex]\rule{200}{2}[/tex]
Let's try the next one:
x values: -1, 0, 1, 2- we add 1 each time
y values: 5, 10, 15, 20- we add 5 each time
[tex]\rule{200}{2}[/tex]
Let's try the third one:
x values: -1, 0, 1, 2- we add 1 each timey values: 15, 18, 20, 21- we add 3, then 2, then 1..
So this table doesn't represent a linear function.
Let's check the fourth one:
x values: -1, 0, 1, 2- we add 1 each time
y values: 1, 2, 3, 4- we add 1 each time
Thus, Option C is the right option.
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
os
10. What is the slope of the line that passes through the pair of points? (1 point)
(-2, 1), (2, 17)
4
O 17
0-15
04
04
Answer:
[tex]\boxed{\sf{4}}}[/tex]
Step-by-step explanation:
Use a slope form.
Slope:
[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{rise}{run} }[/tex]
y₂ = (17)
y₁ = (1)
x₂ = (2)
x₁ = (-2)
Then, rewrite the problem.
Solve.
[tex]\sf{\dfrac{17-1}{2-(-2)}=\dfrac{16}{4}=\dfrac{16\div4}{4\div4}=\dfrac{4}{1}=\boxed{\sf{4} }[/tex]
Therefore, the slope is 4, which is our answer.
I hope this helps you! Let me know if my answer is wrong or not.
if £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after two years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2\implies A=2121.8[/tex]
Answer:
2,121.8
Step-by-step explanation:
2000(1.03)^2
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Q. A circular pie has an area of 706.5 cm? What is the radius of the pie?
answer choices
A. 225 cm
B. 30 cm
C. 15 cm
D. 112.5 cm
Answer:
C. 15 cm
Step-by-step explanation:
The formula to find the area of a circle is: π × r²
But since we need to solve for the radius, we use the formula:
[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]
r = radius
A = area
π = 3.14
Now we substitute the information given in the text into the equation
[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]
Substitute values into the equation
[tex]r = \sqrt{ \dfrac{ 706.5 }{ 3.14 } \phantom{\tiny{!}}}[/tex]
Divide 706.5 by 3.14
[tex]r = \sqrt{ 225 }[/tex]
Take the square root of 225
[tex]r = {15 }[/tex]
So, the radius of the pie is 15 cm
I need help please!!!!!!
Answer:
432 feet^2
Step-by-step explanation:
If we fill in the edges, it'll be 24x8, since 16+2 is 18, and 20+2(2) is 24. 24x18 is 432. Brainliest please.
Find the surface area of the prism. Write your answer as a decimal.
Answer:
49.2 square yards
Step-by-step explanation:
The surface area of a rectangular prism can be found using the formula.
A = 2(LW +H(L +W)) . . . . where L, W, H are length, width, height
A = 2(3×5 +1.2(3 +5)) = 2(15 +9.6) = 49.2 . . . . square yards
PLEASE HELP!! URGENT!
Step-by-step explanation:
258
because there are 360 degrees in a circle. 360 - 102 = 258