Joanie believes that you cannot use cross products to solve the proportion startfraction 50 over 3 endfraction = startfraction 75 over x endfraction for x. she says that if you multiply both sides of the equation by x, you get startfraction 50 x over 3 endfraction = 75. then, if you multiply both sides of the equation by 3, you get 50 x = 75, which is a different equation than you would get if you cross multiplied. what mistake did joanie make in her reasoning?
she assumed that the multiplication property of equality allows her to multiply both sides of the equation startfraction 50 over 3 endfraction = startfraction 75 over x endfraction by x.
she assumed that the multiplication property of equality allows her to multiply both sides of the equation startfraction 50 x over 3 endfraction = 75 by 3.
she assumed that 50 x = 75 is the equation that you get if you multiply both sides of the equation startfraction 50 x over 3 endfraction = 75 by 3.
she assumed that 50 x = 75 is a different equation than you would get if you cross multiplied to solve the proportion startfraction 50 over 3 endfraction = startfraction 75 over x endfraction for x.

If the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)

The expression is given by

56 + 96

First we have to find the GCF of the numbers

Prime factorization

56 = 2×2×2×7

96 = 2×2×2×2×2×3

The GCF(56, 96) = 8

Write the expression using the GCF

56 + 96 = 8(7) + 8(12)

Here we have to apply the distributive property

AB + AC = A(B + C)

Then,

8(7) + 8(12) = 8 (7 + 12)

Hence, if the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)

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The total number of days all crew needs to pour concrete is 6 days consecutive.

Given that,

Total number of crew = 3

Total yards = 175,000

Each crew pour concrete per hour = 1200

Therefore, Total concrete pour per day = 1200 × 3 × 8

                  Total concrete pour per day = 28,800 yard

Total number of days crew pours concrete

          = Total yards / Total concrete pour per day

Total number of days crew pours concrete = 175,000 / 28,800

Total number of days crew pours concrete = 6.076

Total number of days crew pours concrete = 6 days

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Formulated theorem is for any positive integer n,

If n is a multiple of 3, then second player will win in game of taking stones from a heap described above else first player will win.

Total 3 base cases are required.

Proof of the theorem by mathematical induction,

Base case,

For n = 1, the first player must take the only stone and wins.

For n = 2, the first player can take two stones and wins.

For n = 3, the first player can take one stone and leave the second player with two stones, ensuring the second player will lose.

The base cases are true.

Inductive step,

Assume that the theorem is true for all positive integers k ≤ n.

Show that the theorem is true for n+1.

If n+1 is not a multiple of 3, then the first player can take one or two stones to reduce the heap size to a multiple of 3.

Second player will then be in position of having to take last stone from a heap of size that is a multiple of 3 and so will lose.

The first player can always force a win when n+1 is not a multiple of 3.

If n+1 is a multiple of 3, then regardless of how many stones the first player takes.

The second player can always leave the first player with a heap of size that is not a multiple of 3 on their turn.

By the assumption of the theorem,

This means that the second player can force a win.

This implies, the second player can always win when n+1 is a multiple of 3.

Since the inductive step assumes that the theorem is true for all positive integers up to n.

Therefore, the theorem is true for all positive integers n and  needed to prove the base cases for n = 1, 2, and 3.

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It will take Vincent 24 number of days to build the cubby house by himself.

Let's assume that Vincent can build the cubby house alone in h days.

From the given information, we know that Nadia takes 12 days to build the cubby house, and when Nadia and Vincent work together, they can finish it in 8 days.

We can use the concept of "work done" to solve this problem. The amount of work done is inversely proportional to the number of days taken.

Nadia's work rate is 1/12 of the cubby house per day, while the combined work rate of Nadia and Vincent is 1/8 of the cubby house per day.

When Nadia and Vincent work together, their combined work rate is the sum of their individual work rates:

1/8 = 1/12 + 1/h

To solve for h, we can rearrange the equation:

1/h = 1/8 - 1/12

1/h = (3 - 2) / 24

1/h = 1/24

Taking the reciprocal of both sides, we find:

h = 24

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Answer:6.28

Step-by-step explanation:

you multaply 2 feet by 3.14 because diameter is cercumfrence times pie

Answer:

21

BIDMAS

36 divided by 6 = 6

multiply by 2

add 9

Answer:

Area of the rhombus ABCD = 16 square units

Step-by-step explanation:

Area of a rhombus = \(\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})\)

From the graph attached,

Diagonal 1 = Distance between the points A and C

Diagonal 2 = Distance between the points B and D

Length of a segment between (x₁, y₁) and (x₂, y₂) = \(\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2 }\)

Diagonal 1 (AC) = \(\sqrt{(4-0)^2+(-1+1)^2}\) = 4 units

Diagonal 2(BD) = \(\sqrt{(2-2)^2+(3+5)^2}\) = 8 units

Now area of the rhombus ABCD = \(\frac{1}{2}(\text{AC})(\text{BD})\)

                                                       = \(\frac{1}{2}\times 4\times 8\)

                                                       = 16 units²

Therefore, area of the given rhombus is 16 units².

Answer:

$63.54

Step-by-step explanation:

You first need to find how much it costs for one gallon of gas. To do this, you divide the amount of money by the amount of gallons;

$21.15 / 6 gallons = $3.53

For one gallon of gas, it costs $3.53. To find how much 18 gallons would cost, we multiply how much gas/gal costs by 18 gallons.

$3.53 x 18 gallons = $68.54 for 18 gallons of gas

I hope this helps!

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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0.8973 is the probability that the next tornado will occur within the next seven months.

Applying the rule of three, we can infer that since the average number of tornadoes in a year is 3.9, the average number of tornadoes in a nine-month period is 3.9*7/12 = 2.275. It is reasonable to believe that the distribution of tornadoes over time is Poisson. Let's refer to X as the number of tornadoes in a seven-month period. X has a Poisson distribution with a parameter of 2.27.

The probability of X being greater than or equal to 1 is equivalent to the likelihood that the next tornado will occur within the next seven months.. However P(X≥1) = 1-P(X=0), and

\(p(X=0) = (e^{2.275} * 2.275^{0}) / 0!\) = 0.1027  

Thus, the probability that the next tornado comes within the next 7 months is 1-0.1027  = 0.8973.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 7900\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 7900\left(1+\frac{0.023}{1}\right)^{1\cdot 5} \implies A=7900(1.023)^5\implies A \approx 8851.26\)

When s = 0, it will take 20 units of time for the account to double to 2X.

(a) When s = 0, it means the deposit is made at time t = 0. We want to find the time it takes for the account to double to 2X.

To find this time, we need to solve the equation a(t) = 2, where a(t) is the accumulation function.

1 - 0.05t = 2

Simplifying the equation, we have:

-0.05t = 1

Dividing both sides by -0.05, we get:

t = -1 / (-0.05)

t = 20

Therefore, when s = 0, it will take 20 units of time for the account to double to 2X.

(b) When s = 5, it means the deposit is made at time t = 5. We want to find the time it takes for the account to double to 2X.

Using the same equation a(t) = 2 and substituting t = 5, we have:

1 - 0.05(5) = 2

1 - 0.25 = 2

0.75 = 2

This equation is not satisfied, which means the account will not double to 2X when the deposit is made at time t = 5.

(c) The answer in (a) is greater than the answer in (b) because when the deposit is made at time t = 0, the account has more time to accumulate interest and grow compared to when the deposit is made at time t = 5. As time progresses, the effect of compounding becomes more significant, and starting earlier allows for more growth and a shorter time to double the account.

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Answer:

20% increase in her pay

Step-by-step explanation:

It's 20% increased, because it increased by $2, $2 goes into $10 5 times, and if you were to put that into percentages 2 is a fifth of 10 so that would 20%, because 20 is a fifth of 100.

Answer:

It's 20% increased,  

Step-by-step explanation:

because it increased by $2, $2 goes into $10 5 times, and if you were to put that into percentages 2 is a fifth of 10 so that would 20%, because 20 is a fifth of 100.

Answer:

The answer is 100

Step-by-step explanation:

9514 1404 393

Answer:

  (c)  162 cm

Step-by-step explanation:

The centroid divides a median into parts with the ratio 1:2, so RL:LD = 1:2. Then RL:RD = 1:(1+2), and RD = 3RL.

  RD = 3·54 cm

  RD = 162 cm

Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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Answer:

True

Step-by-step explanation:

Just compare the numbers to the dots.

I hope this helps!

pls ❤ and give brainliest pls

Answer:

true

Step-by-step explanation:

The answer is true.

The sum of the exterior angle of the pentagon is 360 degrees.

The polygon above is a pentagon. A pentagon is a polygon with 5 sides.

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. The sum of the exterior angles of a polygon is 360°.

Therefore, the sum of the measure of the exterior angles of the pentagon as shown is 360 degrees.

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Answer:

======================

The two given angles form a linear pair.

Sum of the two angles is 180°, set equation and solve for e:

Answer: If this isn't a trick question it is $68.60

Step-by-step explanation: You just multiply the 98 cents by the 70 songs.

Answer:

68. 60

Step-by-step explanation:

You have to put the 0 from 70 first then times 8x7 then 9x7 giving you your answer

\(\huge\mathbb\purple{AnSwEr}\)

\(\huge❤\bold\red{Hello}❤\)

Hey mate 1. $246,000 2. $20,66,610 is your Answer

\(My \: pleasure \: to \: help \: you \: anytime.\)

\(Mark \: me \: as \: brainliest .\)

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Answer:

\(x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}\)

Step-by-step explanation:

1) Move all terms to one side.

\(2x^{3} -x^{2} -3x-210=0\)

2) Factor \(2{x}^{3}-{x}^{2}-3x-210\) using Polynomial Division.

1 -  Factor the following.

\(2x^{3} -x^{2} -3x-210\)

2 -  First, find all factors of the constant term 210.

\(1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210\)

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

\(2*1^{3} -1^{2} -3*1-210=-212\)

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

\(2(-1)^{3} -(-1)^{2} -3*-1-210=-210\)

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

\(2*2^{3} -2^{2} -3*2-210=-204\)

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

\(2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224\)

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

\(2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174\)

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

\(2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264\)

Substitute 5 into x. Since the result is 0, x-5 is a factor..

\(2\times {5}^{3}-{5}^{2}-3\times 5-210 =0\)

------------------------------------------------------------------------------------------

⇒ \(x-5\)

4)  Polynomial Division: Divide \(2{x}^{3}-{x}^{2}-3x-210\)  by \(x-5\).

                                               \(2x^{2}\)                       \(9x\)                      \(42\)

                                      -------------------------------------------------------------------------

\(x-5\)                               |    \(2x^{3}\)                          \(-x^{2}\)                     \(-3x\)     \(-210\)

                                           \(2x^{3}\)                             \(-10x^{2}\)

                                        -----------------------------------------------------------------------

                                                                             \(9x^{2}\)                \(-3x\)       \(-210\)

                                     --------------------------------------------------------------------------

                                                                          \(42x\)                              \(-210\)

                                                                         \(42x\)                               \(-210\)

                                      -------------------------------------------------------------------------

5)  Rewrite the expression using the above.

\(2x^2+9x+42\)

\((2x^2+9x+42)(x-5)=0\)

3) Solve for \(x.\)

\(x=5\)

4)  Use the Quadratic Formula.

1 - In general, given \(a{x}^{2}+bx+c=0\) , there exists two solutions where:

\(x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}\)

2 -  In this case, \(a=2,b=9\) and \(c = 42.\)

\(x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}\)

3 - Simplify.

\(x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}\)

5) Collect all solutions from the previous steps.

\(x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}\)

please see photo attached

Answer:

20

Step-by-step explanation:

Make 12 into a fraction : 12/1

Then , using division with fractions , flip the 3/5 and multiply 12/1 and 5/3 .

The equation will look like this :

12/1 x 5/3

So 12 x 5 = 60 and 1 x 3 = 3 , making the fraction 60/3

That then simplifies to 20

:)

Answer:

.25

Step-by-step explanation:

37.50/5=7.5

58/8=7.25

7.5-7.25=.25

Answer:

260

Step-by-step explanation:

So first you need to multiply 5 and 37. and the is 5×37 equals 185. So now your gonna multiply 8 by 58 and that is 464. So now that you have those two numbers ( 185, 464 ) your gonna add how ever much you need to get 464. So the closest to get to 464 is gonna be 260 I'm pretty sure.

The constraint(s) to ensure that the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is:

3X3 <= 4X2

This constraint states that the number of 3 bedroom rentals (X3) must be less than or equal to four times the number of 2 bedroom rentals (X2). This ensures that the ratio of 3 bedroom rentals to 2 bedroom rentals does not exceed 4 to 1.

For example, if there are 10 2 bedroom rentals (X2), the constraint would be:

3X3 <= 4(10)
3X3 <= 40

This means that the number of 3 bedroom rentals (X3) cannot exceed 40.

The constraint to ensure the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is 3X3 <= 4X2.

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Answer:

Your answer is: t = 3

83 = 24.5t

73.5 = 24.5t

t = 3

t = tickets

b = 2

m = -2/5

Step-by-step explanation:

Hope this helped : )

Given the probabilities P(A) = 0.7, P(Ac) = 0.3, P(B|A) = 0.4, and P(B|Ac) = 0.8, the joint probabilities can be calculated as follows: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.12, and P(Ac and Bc) = 0.18.

The joint probability P(A and B) represents the probability of events A and B occurring simultaneously. It can be calculated using the formula P(A and B) = P(A) * P(B|A). Given that P(A) = 0.7 and P(B|A) = 0.4, we can multiply these probabilities to obtain P(A and B) = 0.7 * 0.4 = 0.28.

It can be calculated as P(A and Bc) = P(A) * P(Bc|A). Since the complement of event B is denoted as Bc, and P(Bc|A) = 1 - P(B|A), we can calculate P(A and Bc) as P(A) * (1 - P(B|A)) = 0.7 * (1 - 0.4) = 0.42.

Finally, P(Ac and Bc) represents the probability of both event A and event B not occurring. It can be calculated as P(Ac and Bc) = P(Ac) * P(Bc|Ac). Using P(Ac) = 0.3 and P(Bc|Ac) = 1 - P(B|Ac), we can calculate P(Ac and Bc) as P(Ac) * (1 - P(B|Ac)) = 0.3 * (1 - 0.8) = 0.18.

Therefore, the joint probabilities are: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.24, and P(Ac and Bc) = 0.18.

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The Distance - Time graph that represents that represents Charlie's trip is attached accordingly.

A distance-time graph can be used to illustrate the distance traveled by an item moving in a straight line.

The gradient of the line in a distance-time graph equals the speed of the item. The quicker the item moves, the higher the gradient (and the steeper the line).

Some of the uses of the distance-time graph are;

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Answer:

the square root of 49

Step-by-step explanation:

may I please have brainlyest

The cylindrical and spherical coordinates of the point are (\(\sqrt{8}\),0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Rectangular coordinates of a point is written like (x, y, z)

Cylindrical coordinates of a point  is written like (r, θ, z)

Spherical coordinates of a point is written like (p, θ, φ)

First talk about Rectangular vs Cylindrical.

x = rcosθ

y = rsinθ.

z = z

x^2 + y^2  = r^2

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

r^2 = 4+4 = 8.

r = \(\sqrt{8}\)

r = 2\(\sqrt{2}\)

θ = \(tan \inv-1\)(y/x) = \(tan \inv-1\)(2/2) = \(tan -1\)(1) = 45° = 0.78rad .

z = -1.

So Cylindrical coordinates is (r,θ,z) = (\(\sqrt{8}\),0.78,-1).

Now let's us talk about Rectangular vs Spherical Coordinates.

x =  pcosθsinφ.

y= psinθsinφ.

z = pcosφ.

p^2 =  x^2+y^2+z^2.

tanθ = y/x

cosφ = z/p = z/\(\sqrt{x^2+y^2+z^2}\).

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

p = \(\sqrt{x^2+y^2+z^2}\) = \(\sqrt{2^2+2^2+(-1)^2}\) = \(\sqrt{9}\) = 3

θ = \(tan -1\)(y/x) =  0.78rad .

φ = \(cos -1\)(z/p) = \(cos -1\)(-1/3) = 1.91rad

So Spherical coordinates is (3, 0.78rad, 1.91rad).

The cylindrical and spherical coordinates of the point are (\(\sqrt{8}\),0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Given Question is incomplete, Complete Question here

The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,

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