Students took a survey to determine their end of year field trip. The results showed that 120 students wanted to go to an amusement park. This number represents 40% of the students who took the survey. What was the total number of students who took the survey? ​

Let the two number is a and b

so,

product =ab=20

sum of square=[tex]\bold{a^2+b^2=41 }[/tex]

Then,

[tex]\bold{(a+b)^2=a^2+b^2+2ab }[/tex]

[tex]\bold{ (a+b)^2=41+2×40 }[/tex]

[tex]\bold{ (a+b)^2=81 }[/tex]

[tex]\bold{a+b=\sqrt{81} }[/tex]

[tex]\bold{a+b=9 }[/tex]•••••••••(equation I)

Now,

[tex]\bold{(a-b)^2=a^2+b^2-4ab }[/tex]

[tex]\bold{ (a-b)^2=41-4×20 }[/tex]

[tex]\bold{(a-b)^2=41-40 }[/tex]

[tex]\bold{a-b=\sqrt{1} }[/tex]

[tex]\bold{a-b=1 }[/tex]••••••••(equation II)

Now,combine the equation I and equation II

we,get

[tex]\bold{a+b+a-b=9+1 }[/tex]

[tex]\bold{a+\cancel{b}+a\cancel{-b}=10 }[/tex]

[tex]\bold{ 2a=10 }[/tex]

[tex]\bold{a=\dfrac{10}{2} }[/tex]

[tex]\blue{\boxed{ a=5 }}[/tex]

Then,

put the value of a in equation II.

we get that,

[tex]\bold{5-b=1 }[/tex]

[tex]\bold{b+1=5 }[/tex]

[tex]\bold{b=5-1 }[/tex]

[tex]\bold{\boxed{\blue{b=4}} }[/tex]

so,

The two number is 5 and 4.

Answer:

1/2

Step-by-step explanation:

the 2 numbers greater than 4 on a six sided die are 5 and 6, and with the 1, that is 3 numbers, or 3 sides of the die.

3/6 simplifies to 1/2

Answer:

Option 1.

(I don't really have any explanation to add on)

Answer:

the 3th option

Step-by-step explanation:

hope it help you

Step-by-step explanation:

44/13 ÷ -9

44/13 *1/-9

44/-117

The equivalent value of the expression A = 44/13 divided by (-9) = -0.3761

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 44/13 divided by ( -9 (

First, we can simplify 44/13 to a decimal:

44/13 = 3.3846 (rounded to four decimal places)

Then we can divide 3.3846 by -9:

3.3846 / (-9) = -0.3761 (rounded to four decimal places)

Therefore, 44/13 divided by (-9) is approximately equal to -0.3761

Hence , the equation is A = -0.3761

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Answer:

C: (-4,3)

Step-by-step explanation:

2x+x+7=-5

3x+7=-5

3x=-12

x=-4

y=-4+7

y=3

(-4,3)

Answer:

[tex]2160\pi \:\mathrm{ft^3} \approx 6786\:\mathrm{ft^3}[/tex]

Step-by-step explanation:

The volume of a cylinder is given as:

[tex]r^2\pi\cdot h[/tex].

Thus, the difference of the cylinders' volumes are:

[tex]|18^2\cdot 20\cdot \pi - 12^2\cdot 30 \cdot \pi|\approx \fbox{$6785.84\:\mathrm{ft^3}$}[/tex].

Since you've said [tex]6785.8[/tex] is not being accepted as an answer, please check all instructions to see if there are directions asking you to specifically round your answer. If not, you can ask your teacher/instructor what they're looking for.

Answer:

2/3

Step-by-step explanation:

Given:

Consider the below figure attached with this question.

To find:

The per perimeter of the isosceles trapezoid. Round all figures to the nearest hundredths place.

Solution:

Consider the isosceles trapezoid is ABCD.

Draw two perpendicular from C and D to  AB as shown in second figure.

Now, CDEF is a rectangle,

[tex]EF=CD=9\text{ ft}[/tex]

[tex]AB-EF=13-9[/tex]

[tex]AB-EF=4\text{ ft}[/tex]

It is an isosceles trapezoid, so [tex]\Delta ADE\cong \Delta BCF[/tex].

[tex]AE=BF=\dfrac{4}{2}=2\text{ ft}[/tex]

Now,

[tex]AE^2+DE^2=AD^2[/tex]         [Pythagoras theorem]

[tex]2^2+4^2=AD^2[/tex]

[tex]4+16=AD^2[/tex]

[tex]\sqrt{20}=AD[/tex]

[tex]AD=BC\approx 30.94[/tex]          [Isosceles trapezoid]

Find the perimeter of the figure.

[tex]Perimeter=AB+BC+CD+AD[/tex]

[tex]Perimeter=13+4.47+9+4.47[/tex]

[tex]Perimeter=30.94\text{ ft}[/tex]

Therefore, the correct option is c.

Shorter Version: C lol

Answer:

1) y+6 or 6+y 2) 12 x n = x 3) 24 + b = x 4) x - 18 5) n - 5 6)a / 3 or 3 / a

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

dice have 6 sides and the coin has 2 sides, so u multiply 6x2 to get your denominator 12. you are trying to get 1 side of the dice, and 1 side of the coin so the numerator is 1. when put together you get the fraction 1/12

Answer:

D. tossing a coin 3 times

Answer:

She should multiply her current balance by 1.052.

Step-by-step explanation:

Her investment is an account with a simple interest of 5.2% per year.

So in one year, she will have 100% + 5.2% = 105.2% of her initial amount. To find the multiplier, we divide by 100%. So

105.2%/100% = 1.052

She should multiply her current balance by 1.052.

Answer:

4 2/15

Step-by-step explanation:

4 x 9 = 36 3 x 5 = 15 5 x 9 = 45

36/45 + 15/45 = 51/45 = 1 6/45

1 + 2 + 1 = 4 + 6/45 = 4 6/45= 4 2/15.

Answer:    R-squared (pronounced ARRRrrr-squared)

LOL, hope it helped.

Answer: R

That's my answer

Answer: e. II and III

II. The mean of sample G, TG, is a point estimator for the mean of the population.

III. The mean of sample H, my, is a point estimator for the mean of the population.

Step-by-step explanation:

The point estimate simply means deriving a single value from a sample which could be used as a good or close estimate of the population from which the sample was drawn. A point estimator for the mean in the scenario above means a best guess of the mean value of the population from the sample mean.

Hence, since both sample G and H are drawn from the same population, both TG and TH which are mean of sample G and H can be used as a point estimator for the mean of the population.

However, it is does not necessarily mean that either the sample mean TG or TH must be equal to the population mean

Answer: 37.5 rounded it would be 38

Step-by-step explanation:

Answer:

a. 0.99995 = 99.995% probability that one of the two parachutes deploys

b.0.04995 = 4.995% probability that the backup parachutes deploys

Step-by-step explanation:

a. What is the probability that one of the two parachutes deploys?

Either the first deploys(with probability 95%), or the first does not deploy(probability 5%) and the second does(probability 99.9%). So

[tex]p = 0.95 + 0.05*0.999 = 0.99995[/tex]

0.99995 = 99.995% probability that one of the two parachutes deploys

b. What is the probability that the backup parachutes deploys?

The first does not deploy(probability 5%) and the second does(probability 99.9%). So

[tex]p = 0.05*0.999 = 0.04995[/tex]

0.04995 = 4.995% probability that the backup parachutes deploys

Answer:

Truw

Step-by-step explanation:

It is exceptional

Answer:

yes

Step-by-step explanation:

using elimination you can see every other answer is definitely wrong leaving you with just one which is 2UX

9514 1404 393

Answer:

  2UX (your answer is correct)

Step-by-step explanation:

One way to define a parabola is as the set of points equidistant from the focus and directrix.

That means the distance from W to the directrix must be the same as the distance WU. Since the parabola is symmetrical and WU is parallel to the directrix, we have WU = UT = UX. So the double length WT is double the distance UX:

  WT = 2UX

sorry i don't know

sorry

sorry

Answer:

Step 1 16+24-18

Step 2) 22

Step-by-step explanation:

Step-by-step explanation:

diameter is 8•5

radius is d/2

8•5/2

=4•25

surface area = 4πr^2

4×22/7×4•25×4•25

=1589•5/7

=227•1

Volume= 4/3πr^3

4/3×22/7×4•25×4•25×4•25

4/3×22/7×76•76

=321•7

Hope it helps

plz mark as brainliest

Answer:

2

Step-by-step explanation:

You don't measure cereal in the others because feet, meters and millimeters are too big. Hope this helps.

Answer:

Step-by-step explanation:

50 percent of 39=

39/2=19.50

Answer:

its 1/3

Step-by-step explanation:

please mark it as brainliest!!<3

Answer:

We conclude that the common difference of the Arithmetic sequence is: 1/3  

Step-by-step explanation:

Given the Arithmetic sequence

1/2, 5/6, 7/6, 3/2, 11/6

We know that an Arithmetic sequence has a constant common difference.

Let us compute the common difference 'd' of all the adjacent terms

[tex]\frac{5}{6}-\frac{1}{2}=\frac{1}{3},\:\quad \frac{7}{6}-\frac{5}{6}=\frac{1}{3},\:\quad \frac{3}{2}-\frac{7}{6}=\frac{1}{3},\:\quad \frac{11}{6}-\frac{3}{2}=\frac{1}{3}[/tex]

The difference between all the adjacent terms is the same and equal

Therefore,

[tex]d=\frac{1}{3}[/tex]

Hence, we conclude that the common difference of the Arithmetic sequence is: 1/3  

Answer:

they are perpindicular because they intersect at a right angle

Step-by-step explanation:

Answer:

The lines y=−4 and x=−1 are perpendicular.

Step-by-step explanation:

Given the lines

y=−4

x=−1

The equation y = -4 indicates that the line is horizontal because the value of y remains constant no matter what the value of x is. We also know that the slope of a horizontal line is zero.

In other words, there is no change in y-value i.e. (y₂-y₁) = 0.

Thus, the slope of the horizontal line y = -4 is zero.

Therefore, the slope of y = -4 is: m₁ = 0

The equation x = -1 indicates that the line is vertical because the value of x remains constant no matter what the value of y is. We also know that the slope of a vertical line is undefined or ∞.

In other words, there is no change in x-value i.e. (x₂-x₁) = 0.

Thus, the slope of the vertical line x = -1 is zero.

Therefore, the slope of x = -1 is: m₂ = ∞.

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.

As the slope of line y = -4 is: m₁ = 0

Thus, the slope of the the new perpendicular line = m₂ = – 1/m = -1/0 = ∞

Therefore, the lines y=−4 and x=−1 are perpendicular.

ALSO:

From the attached graph, it is clear that:

It is clear that both lines are perpendicular as they are meeting at a right angle.

Therefore, the lines y=−4 and x=−1 are perpendicular.

Answer:

g(2) = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = x²

g(2) is x = 2

Step 2: Evaluate