Zack has two strings of equal length. One string is red the other is yellow. After cutting 2.5 meters of the red string and 3.8 M of the yellow string, the length of the red string is 1.5 times that of the yellow strain. Find the original length of the yellow string.

Variables represent unknowns.  They are often letters (like x) but can also be other symbols like Greek numerics.

Hope this helps!!

Answer: he is right it is variables that are the unknown

Step-by-step explanation:

Answer:

D. No the answer is not reasonable. it should be about 10 pounds.

I took the test.

Answer:

No, the answer is not reasonable. It should be about 10 pounds.

Step-by-step explanation:

Given,

The quantity of hot dog bought by Jill's club = [tex]4\frac{2}{5}[/tex] pounds,

Hot dog = [tex]3\frac{1}{2}[/tex] pounds

Hamburger = [tex]2\frac{3}{10}[/tex] pounds

So, the total quantity of meat they bought

[tex]=4\frac{2}{5}+3\frac{1}{2}+2\frac{3}{10}[/tex]

[tex]=\frac{22}{5}+\frac{7}{2}+\frac{23}{10}[/tex]

[tex]=\frac{44+35+23}{10}[/tex]  ( Adding fractions ),

[tex]=\frac{102}{10}[/tex]

[tex]=10.2\text{ pounds}[/tex]

Since, [tex]8\frac{1}{2}=\frac{17}{2}=8.5[/tex]

[tex]\implies 8.5\neq 10.2[/tex]

Hence, the student's answer is not reasonable it should be about 10 pounds.

Third option is correct.

Answer:

A.  (4000/3)  π cubic units

Step-by-step explanation:

The volume of a sphere is given by V = (4/3) π r³

Since this sphere has a radius of 10, we can find its volume by inserting the value of the radius in the formula:

[tex]V = \frac{4}{3} \pi 10^{3} = \frac{4}{3} * 1000 * \pi =\frac{4000}{3} \pi[/tex]

Since all the possible answers are given with π in them, we can stop the calculation there and say the volume is (4000/3)  π cubic units.

Answer:

(4000/3)[tex]\pi[/tex] units³

Step-by-step explanation:

~apex

The rocket exceed the height of 500 ft in 1.46 seconds or 8.43 seconds.

Standard form of the quadratic equation in the variable x is an equation of the form a[tex]x^{2}[/tex] + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Any equation of the form P(x) = 0, Where P(x) is a polynomial of degree 2, is a quadratic equation.

Given equation of height is:

h(t)= -[tex]16t^{2} +160t+300[/tex]

Now, the exceeded to 500 feet.

So,

-[tex]16t^{2} +160t+300[/tex]=500

16[tex]t^{2}[/tex] -160 t +200=0

Now, solve for t: a=16, b= -160, c= 200

D= [tex]\sqrt{b^{2}-4ac }[/tex]

 = [tex]\sqrt{(-160)^{2}-4*16*200 }[/tex]

 = [tex]\sqrt{12800 }[/tex]

 = 80√2

As D>0 then,

x= [tex]\frac{-b\pm \sqrt{b^{2}-4ac }}{2a}[/tex]

x= (160 ±80√2)/32

x=  (160 +80√2)/32   or x= (160 -80√2)/32

So, x= 8.43 and x=1.46

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given sides,

a=36

b=45

c=27

From cosine law,

cosA=

[tex] \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} \\ = \frac{ {45}^{2} + {27}^{2} - {36}^{2} }{2 \times 45 \times 27} \\ = \frac{3}{5} = 0.6[/tex]

or, A= cos^-1(0.6)=53.13°

similarly, cosB=

[tex] \frac{ {a}^{2} + {c}^{2} - {b}^{2} }{2ac} \\ = \frac{ {36}^{2} + {27}^{2} - {45}^{2} }{2 \times 36 \times 27} \\ = 0[/tex]

or, B= cos^-1(0)=90°

Since, B=90, the given triangle is right angled triangle.

Answer:

  96°

Step-by-step explanation:

In a cyclic quadrilateral (one inscribed in a circle), opposite angles are supplementary. That means the angles marked (6m+13)° and (4m+7)° have a total value of 180°:

  (6m+13) +(4m+7) = 180

  10m +20 = 180 . . . . . . . . collect terms

  m +2 = 18 . . . . . . . . . . . . .divide by 10

  m = 16 . . . . . . . . . . . . . . . subtract 2

∠M = 6m° = 6·16° . . . . . . . use the value of m in the expression for ∠M

∠M = 96°

Answer:

4

Step-by-step explanation:

Step-by-step explanation:

Arc length is defined as:

s = rθ

where r is the radius and θ is the angle in radians

A unit circle has a radius of 1, so the arc length is equal to the radian measure of the angle.

The radian measure determines the arc length on the unit circle using the formula s = θ for a unit circle (radius = 1). Radians, being a ratio of arc length to radius, allow for direct conversion between angle and arc length, facilitating calculations and conversions between radians and degrees.

The radian measure of an angle can determine the arc length on the unit circle by using the formula arc length (s) = radius (r) × angle in radians (θ). Since the unit circle has a radius of 1, this simplifies to s = θ. The concept of radians is crucial here; a radian is defined as the ratio of the arc length to the radius of the circle, making it a dimensionless unit. This relationship remains constant regardless of the circle's size, meaning the radian measure directly gives the arc length on the unit circle.

For a full revolution of 2π radians (360 degrees), the arc length is equal to the circumference of the circle, which is 2πr. In the case of the unit circle, this equates to an arc length of 2π. This principle allows for the conversion between radians and degrees, and calculation of arc lengths for any given angle measured in radians.

Answer: The answer is a: 40

Step-by-step explanation:  

Answer:

true if that is the answer your looking for

Step-by-step explanation:

Answer:

0.22

Step-by-step explanation:

The point estimate is simply the middle of the confidence interval.

p = (0.195 + 0.245) / 2

p = 0.22

Its the second graph. An expert above explains why its the second one.

Answer:

138 cm³

Step-by-step explanation:

Given in the question that base of the rectangular prism = 36 cm²

Height of the prism = 3 5/6 cm = 23/6

We know that the volume of a rectangular prism with base area B and height H is given by

Plug values in the formula above to find the volume of the prism

Volume = 36(23/6)

              = 6(23)

              = 138 cm³

So the volume of prism = 138 cm³

Answer:

Required logarithmic function is :

[tex]f\left(x\right)=\log_3\left(x\right)[/tex]

Step-by-step explanation:

Given that table for the logarithmic function is:

x f(x)

9 2

27 3

81 4

which can be rewritten as:

x f(x)

3^2 2

3^3 3

3^4 4

Which are basically powers of 3

Hence required logarithmic function is :

[tex]f\left(x\right)=\log_3\left(x\right)[/tex]

Answer:

3.4

Step-by-step explanation:

Standard deviation of a population is defined as:

σ² = ∑(xᵢ − μ)² / n

The standard deviation of a sample is defined as:

s² = ∑(xᵢ − x)² / (n - 1)

It's not clear which one we have, so let's calculate both.

First, we must find the mean.

μ = (5+12+15+10+12+6+8+8) / 8

μ = 9.5

Now we find the squares of the differences:

(5-9.5)² + (12-9.5)² + (15-9.5)² + (10-9.5)² + (12-9.5)² + (6-9.5)² + (8-9.5)² + (8-9.5)²

= 80

Divide by n:

σ² = 80 / 8

σ² = 10

And take the square root:

σ = √10

σ ≈ 3.2

That's not one of the answers, so let's try the standard deviation of a sample instead of a population.

Instead of dividing by n, we'll divide by n-1:

s² = 80 / 7

And take the square root:

s = √(80/7)

s ≈ 3.4

So that must be it.

The probability of each event occurring does not affect the probability of the other event occurring

I am not sure about the numbers you are working with, but you can use this to help you out:

[tex]p(a \: and \: b) = p(a) \times p(b)[/tex]

Good luck!

Answer:

1,005 cm³

Step-by-step explanation:

The volume of a cylinder can be calculated by multiplying the area of its base times the height. It is calculated as follows:

V = πr²h

V = π(8/2)²(20)

V = 1005.31 cm³

Answer:

1,005 cm³

Step-by-step explanation:

because im the goat

Answer:

In interval notation it is  ( -∞, ∞).

Step-by-step explanation:

All values of x can be input to this function.

Answer:

you multiply it by 100 since there are 100 cents in a dollar. so, 24804 cents. it stays at 4 because 2 is less than 5

Step-by-step explanation:

Answer:

$-248.04.

Step-by-step explanation:

This is the correct answer to your question.

Hope this helps!!!

Kyle.

Answer:

400 yards

Step-by-step explanation:

(√A)4

(√10,000)4

(100)4

400

Hope This Helps! :D

25.50 = 7d + 2p

52.50 = 5d + 10p

These are the two equations we're going to use to determine the price of popcorn.

First we need to eliminate one set of variables. Let's eliminate the drinks.

127.50 = 35d + 10p

-367.50 = -35d + -70p

-240 = 0d - 60p

-240 = -60p

P = 4.00

So, popcorn is $4, right? Let's keep working on the problem so we can double check...

So, now let's add the $4 as the variable for P.

25.50 = 7d + 8

52.50 = 5d + 40

17.50 = 7d

12.5 = 5d

d = 2.5

d=2.5

This checks out! Since both equations state that drinks are 2.50, that means we have the right pricing for popcorn... $4.00

Popcorn is $4.00, drinks are $2.50

Hope I could help! :)

Answer:

The mean of the outcomes is 0.52.

Step-by-step explanation:

Multiply each possible outcome {0, 1, 2, 3} by the respective probability, and then add up the four products:

0·0.53 + 1·0.43 + 2·0.03 + 3·0.01.  This comes out to:

     0     +    0.43  + 0.06 + 0.03 = 0.52

The mean of the outcomes is 0.52.

The mean of the outcomes will be equal to 0.52.

Mean is defined as the ratio of the sum of the number of data sets to the total number of data.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Multiply each possible outcome {0, 1, 2, 3} by the respective probability, and then add up the four products:

0·0.53 + 1·0.43 + 2·0.03 + 3·0.01.  

0+0.43  + 0.06 + 0.03 = 0.52

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Answer:

Question 1: x = 0,6,4

Step-by-step explanation:

#1. If we let x be the side of the cut-out square, the formula for the volume of the box is

[tex]\text{Volume} = (12 - 2x)(8 - 2x)(x).[/tex]

Expanding gives us

[tex]\text{Volume} = 4x^3 - 40x^2 + 96x. [/tex]

To find the zeros, we need to set the equation to 0, and the values of x that would result to zero would be:

[tex]x = 0, 6, 4[/tex]

As how it is told 'he' wanted to make a box with no lid for his marble connection, 'he' wants to cut out four "Identical" squares from all of the corners of the sheet (which I'm assuming is that there is four corners) and by doing so he then wants to fold all the sides...

So he buys one that is 8 by 12 inches, so you can draw a box that is (8, 12) put an 'x' at all four corners and 'cut' it the corners out.

Here's the formula that you can use... Which could be either one I guess..

-Cube = a 3

-- a is the side length

-Rectangular prism = a * b * c

-- a, b, c are the length, width, and height

The volume of a cube is side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed. If a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches.

Once you found a function I think you should use the quadratic equation, which is- y=x2-20x+96

And you could use that equation to graph it out... But if they want it to be the volume of 12 cubic inches then er-... Yeah that's were i'm stumped at... My apologies..

what pyramid???????

i think you forgot the pyramid

Answer:

The answer is 11

Step-by-step explanation:

To solve the expression we must use order of operations following the memotecnic rule PEDMAS that states the order of operations. First solve parenthesis, then exponents, then divisions and multiplications from left to right and finally additions and subtractions from left to right . Following this rule we have:

30-2(7+2)-1

First parenthesis

30-2*(9)-1

There are no exponents. There are no divisions so we do multiplications first

30 -18 -1

There are no additions we only do the remaining subtractiosn form left to right

30-18-1= 12-1= 11

Answer:

11

Step-by-step explanation:

Answer:

And step-by-step explanation

Answer:

x = 46°

Step-by-step explanation:

The angle 69° and z form a straight angle and are supplementary, thus

z = 180° - 69° = 111°

The sum of the 3 angles in a triangle = 180°, hence

x = 180° - (111 + 23)° = 180° - 134° = 46°

Answer:

I believe the answer is 110.

Answer:

Step-by-step explanation:

In this problem we need to use the Inscribed Angle theorem, which states that an inscribed angle is one-half its subtended arc.

[tex]\angle C=\frac{1}{2}arc(DB)=70\°[/tex]

Then, we use the theorem about a cyclic quadrilateral, which is an inscribed quadrilateral: "the opposite angles in a cyclic quadrilateral are supplementary".

[tex]\angle C + \angle A = 180\°\\\angle A = 180\° - \angle C\\\angle A = 180\° - 70\° \\\angle A = 110\°[/tex]

Therefore, the answer is 110°

Answer:

there are several possible answers child 1=5.50

child 2=5.03

child 3=5.06

child 4=3.99

child 5=3.51

Step-by-step explanation:

23.09 / 5 = £4.61 = 1 share

4.61 * 3 = 13.83

4.61 * 2 = £9.22

13.87 / 3 = 4.62

9.22 / 2 = 4.61

solving simultaneously

let equation 1 be -3-3y=12x

let equation 2 be -5-y=2x

equation 2 make y subject of formula=> y=-5-2x

replace (y=-5-2x) in equation 1

-3-3(-5-2x)=12x

solve for x

x=2

replace x=2 in equation 2

y=-5-2(2)

y=-9

Therefore, x=2 y=-9

Answer:

Step-by-step explanation:

To calculate the theoretical probability here, we need three inputs:  1) the number of trials (which here is 7); the probability of success (which here is 0.75); and an integer representing the particular outcome (which here would be r:  {0, 1, 2, 3, 4, 5, 6, 7}.

(a)  Most of today's calculators have probability distribution functions built in.  I've used binompdf(n,p,r) here.  i. P(2) = 0.012 is correct; it's the result of typing in binompdf(7,0.75,2).  ii. P(3) = 0.058 is correct.  iii. P(4) = 0.005  is false; this probability is 0.173.  iv. P(5) = 0.015 is false.   v.  P(6) = 0.311 is correct.

(b) The probability that at least four trials are successful is equivalent to P(4) + P(5) + P(6) + P(7).   Another way in which to calculate this would be to add up P(0) + P(1) + P(2) + P(3) and subtract the resulting sum from 1.00:  That comes to:  1 - (0.000 + 0.001 + 0.012 + 0.058), or 1 - 0.071, or 0.929