The cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base are of the cylindrical container is 154 sq cm, what is the base area of the cuboidal container?

Answers

Answer 1

Note that where the cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base area of the cylindrical container is 154 sq cm, the base area of the Cuboidal Container is 15.2

What is the justification for the above?

Let the height of the cylinder and cuboidal container be h m

We know that the base of the cylinder container is given as: 154 sq cm.

Recall that the volume for a cylinder is = Base x Height

That means in this case:

The volume for the cylinder is = 154 x Height

Thus,

1/2 * 154h = 1/3h³

77h =  1/3h³; divide both side by h to get

77 = 1/3h²

Collecting like terms and make h subject of the formula, we have;

h² = 77 * 3

h² = 231

h = √231

h= 15.1986841536

h = 15.199 or [tex]\approx[/tex] 15.2

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Related Questions

Factor problems 1-4 by finding the GCF.

1. 4x3 – 12x2 + 4x

A. 4x(x2 – 3x + 1)
B. 4x(4x2 – 3x + 1)
C. 4x(4x2 – 3x - 1)
D. 4x(x2 – 6x + 1)
E. 2x(2x2 – 6x + 2)
F. This polynomial cannot be factored using the GCF method.
2. 9x4 + 4x3 - 27x2 + 12x

A. x(9x3 + 4x2 + 27x + 12)
B. x(9x3 + 4x2 - 27x + 12)
C. x(9x4 + 4x3 – 27x2 + 12x)
D. x4(9x3 + 4x2 + 27x + 12)
E. x(9x4 + 4x3 - 27x2 + 12x)
F. This polynomial cannot be factored using the GCF method.
3. x2 – 3x + 4

A. x(x – 3)
B. x(x + 3)
C. x(x – 1)
D. x(x – 7)
E. x(x + 7)
F. This polynomial cannot be factored using the GCF method.
4. 17x5 + 51x2 – 34

A. 17x5 + 3x2 + 2
B. 17(x3 + 3x2 + 2)
C. 17(x4 + 3x2 + 2)
D. 17(x5 + 3x2 – 2)
E. x5 + 3x2 – 2
F. This polynomial cannot be factored using the GCF method.
Factor problems 5 - 8 by grouping.

5. x2 – 2x + 1

A. (x – 1)(x – 1)
B. (x – 1)(x + 1)
C. (x + 1)(x – 1)
D. (x + 1)(x + 1)
E. (x + 2)(x – 1)
F. This polynomial cannot be factored by grouping.
6. x2 + 2x – 15

A. (x - 5)(x – 3)
B. (x + 5)(x + 3)
C. (x + 5)(x – 3)
D. (x - 5)(x + 3)
E. (x + 15)(x – 1)
F. This polynomial cannot be factored by grouping.
7. x2 – 3x – 18

A. (x + 3)(x + 6)
B. (x + 3)(x - 6)
C. (x - 3)(x - 6)
D. (x - 3)(x + 6)
E. (-x + 3)(x + 6)
F. This polynomial cannot be factored by grouping.
8. 8x2 + 47x + 28

A. This polynomial cannot be factored by grouping.
B. (3x + 7)(5x - 4)
C. (3x - 7)(5x - 4)
D. (3x + 7)(-5x + 4)
E. (-3x + 7)(-5x + 4)
F. (3x + 7)(5x + 4)

Answers

The factor of the polynomial expression 4x^3 – 12x^2 + 4x by using GCF method is  4x(x^2 - 3x + 1).

What is a factor of a number?

The factors of a given number are those numbers that are divisible by the given number without a remainder.

By using the GCF method in an algebraic, i.e. the factors of the algebraic equation will be dependent on the greatest common factor.

From the given information, we are to factorize the following expression by using the GCF method as follows.

1.

4x^3 – 12x^2 + 4x

Here; the common expression in all the three variables is 4x. So, we have:

= 4x(x^2 - 3x + 1)

Option A is correct

2.

9x^4 + 4x^3 - 27x^2 + 12x

The common expression here is (x); So,

= x(9x^3 +4x^2 - 27x + 12)

Option B is correct

3.

x^2 - 3x + 4

This polynomial expression cannot be factored.

Option F is correct.

4.

17x^5 + 51x^2 - 34

= 17(x^5 + 3x^2 - 2)

Option D is correct.

The factorization of a quadratic equation (polynomial expression) in the form (ax^2 + bx + c) by grouping results into two factors that if multiplied together result back into the original equation.

Given that:

5.

x^2 – 2x + 1

Factors are two numbers that if the multiplied result in (ac) and if added it gives us (b)

By grouping, the polynomial expression is:

= (x - 1)(x - 1)

Option A is correct

6.

x^2 + 2x - 15

= (x + 5) (x - 3)

Option C is correct

7.

x^2 – 3x – 18

=(x + 3)(x - 6)

Option B is correct

8.

8x^2 + 47x + 28

= This polynomial expression cannot be factored in as it contains rational numbers.

Option A is correct.

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The number of marriage licenses issued by Clark County Nevada, the county where Las Vegas is located, has been
decreasing since the year 2000:
According to the model, how many marriage licenses were issued in 2003? Round your answer to the nearest hundred.
You must find the linear regression equation first.

Answers

The number of marriage licenses were issued in 2003 is 21586.

According to the statement

we have to find the number of marriage licenses were issued in 2003

and the given equation is y=3.405x^2-17674x+21533000

And in this equation x represent the time

And Y represent the number of marriage certificate issued.

So, in given equation

y=3.405x^2-17674x+21533000

we fill the value of X and find the value of Y means tne number of marriage license is issued in 2003

We know that X = 3 from 2000 to 2003

Then put X=3 in the given equation.

Then

This is the equation (1) represent the change

y=3.405(3)^2-17674(3)+21533000 -(1)

y = 30.645+53022+21533000

y = 21586052.645

On nearest hundred the value becomes 21586.

So, The number of marriage licenses were issued in 2003 is 21586.

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DISCLAIMER: The question was incomplete. please find the full content below.

QUESTION:

According to the model, how many marriage licenses were issued in 2003? Round your answer to the nearest hundred.

The number of marriage licenses issued by Clark county Nevada, the county where Las Vegas is located, has been decreasing since the year 2000. This can be modeled by y=3.405x^2-17674x+21533000 where x is the year and y is the number of marriage licenses issued.

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Answer: A. 137,000

Step-by-step explanation: I did the quiz.

Does anyone know the answer to this?

Answers

Answer: equation: y=-4x+1

slope: -4

y intercept:1

Determine the number of solutions for the equation shown below.
4x+6= 4x+6
Ο Α. 0
OB. Infinitely many
* O C. 1
OD. 2

Answers

B) it’s infinite you can put -30 in as x and still get the same answer on the other side you could also put x as zero and get 6 as an answer the answer is infinite

a. How many bushels of corn, if any, will the United States export or import at the prices below?
At $1, it will (import, export, or neither import or export )
___bushels.

b. How many bushels of corn, if any, will the United States export or import at the prices below?
At $2, it will (import, export, or neither import or export )
____bushels.

c. How many bushels of corn, if any, will the United States export or import at the prices below?
At $3, it will (import, export, or neither import or export )
____ bushels.

d. How many bushels of corn, if any, will the United States export or import at the prices below?
At $4, it will (import, export, or neither import or export )
____ bushels.

e. How many bushels of corn, if any, will the United States export or import at the prices below?
At $5, it will (import, export, or neither import or export )
____ bushels.

2.

a. Use this information to construct the U.S export supply curve and import demand curve for corn

b. Suppose that the only other corn-producing nations is France, where the domestic price is $4. Which country will export corn and which country will import it

The United Stated will import corn France will export it

The United States will export corn and France will import it

Neither country will import or export corn.

Answers

At $1, the United States will import 15,000 bushels of corn.At $2, the United States will import 7,000 bushels of corn.At $3, the United States will neither import nor export any bushels of corn.At $4, the United States will export 6,000 bushels of corn.At $5, the United States will export 10,000 bushels of corn.

The number of bushels of corn.

Based on the graph which depicts the United States domestic market for  corn at different prices, we can logically deduce the following information:

At $1, the United States will import 15,000 bushels of corn.At $2, the United States will import 7,000 bushels of corn.At $3, the United States will neither import nor export any bushels of corn.At $4, the United States will export 6,000 bushels of corn.At $5, the United States will export 10,000 bushels of corn.

Assuming France is the only other corn-producing nations at a domestic price of $4, we can reasonably infer that the United States will export corn while France will import it.

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3 + b/d

HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Fractions are mathematical expressions that relate two numbers as a quotient. Thus the answer to this question is:  [tex]\frac{3d + b}{d}[/tex]

Fractions are expressions in a form of a quotient that relates one number to another number. The two numbers can be classified as either the numerator or the denominator. The number above the division line is the numerator, while that below the line is the denominator. Some types of fractions are proper fractions, improper fractions, and mixed fractions.

A given fraction can undergo basic arithmetic operations when two or more are involved. Also, a fraction can be added to one another, or subtracted from a whole number.

The given expression in the question involves the addition of a whole number (3), to a fraction (b/d).

Given: 3 + b/d

The LCM is d, thus;

3 + b/d = [tex]\frac{3d + b}{d}[/tex]

Therefore, the required answer is: [tex]\frac{3d + b}{d}[/tex]

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3. Mr. Black's pay increased by 15% when he got a raise, bringing his new salary to $184. What was Mr. Black's original pay? ​

Answers

Answer:

$160

Step-by-step explanation:

115% = $184

100% = X

let X be the original salary

(X is unknown)

115% = $184

100% = X

cross mutiply

115 x X = 100 x 184

115X = 18400

X = 18400 divided by 115

X = $160

therefore,Mr Black's original salary before increased by 15% was $160

hope am helpful.

184/x = 115/100
184*100=18400
18400=115x
18400/115=160
x=160

how to find n if sn=969 of A.p,a1=9 and d=6​

Answers

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍

Nathan shares out 12 sweets he gives yasmin 1 sweet for 3 sweets he buys how many sweets does nathan get

Answers

Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.

How many sweets does Nathan gets?

Given that, Nathan shares out 12 sweets, he gives Yasmin 1 sweet for 3 sweets he buys.

Let the sweet be represented by x

For each x sweet for Yasmin, Nathan gets 3x sweets

Hence

x + 3x = 12

We solve for x

4x = 12

x = 12/4

x = 3

Hence;

Yasmin gets x sweet = 3

Nathan gets 3x sweets = 3 × 3 = 9

Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.

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Find sec, tan 0, and sin 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
0
4
5

Answers

The exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

How to determine the trigonometric ratios

From the figure, we have the values of the sides to be;

opposite side = 5Adjacent side = 4

Let's use Pythagorean theorem to find the hypotenuse(x)

Hypotebuse square = opposite side square + adjacent side square

Substitute the values deduced from the figures given

x² = 5² + 4²

x² = 25 + 16

x² = 41

x = [tex]\sqrt{41}[/tex]

x = 6. 4

sin θ = opposite/hypotenuse

Substitute the values

sin θ = 5/ 6. 4

tan θ = opposite/ adjacent

Substitute the values

tan θ = 5/ 4

sec θ = hypotenuse/ adjacent

substitute the values

sec θ = 6. 4/ 4

Thus, the exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

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How do you solve for m?

m= −(4+m)+2

Answers

Answer:

[tex]\bf m = - 1[/tex]

Step-by-step explanation:

[tex]\bf m= −(4+m)+2[/tex]

First of all, let's Rearrange the given terms :-

[tex]\bf m = - ( m +4) + 2[/tex]

Now, let's distribute:-

[tex]\bf m = - m - 4 + 2[/tex]

Add numbers -4 + 2 = -2

[tex]\bf m = - m - 2[/tex]

Add m to both sides, and combine like terms :-

[tex]\bf 2m = - 2[/tex]

Divide both sides by 2 :-

[tex]\bf m = - 1[/tex]

m= -(4+m)+2
m= -4-m+2
2m= -2
m= -1

Hope it helps : )

Please draw the number line and show me if possible:)

Answers

The solution to the given inequality expression is expressed as x ≥ 6

Solving inequalities

Given the inequality expression shown below;

5x-9/7≥3

Cross multiply

(5x -9)≥7(3)

Expand

5x-9≥21

Add 9 to both sides

5x ≥ 21 + 9

5x ≥ 30

x ≥6

The solution to the given inequality expression is expressed as x ≥ 6

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Solve p/-1+ 17 = 13 for p.

Answers

Answer: 208

Step-by-step explanation:

[tex]\frac{p}{-1+17} =13[/tex]

[tex]\frac{p}{16} =13[/tex]

[tex](16)\frac{p}{16} =13(16)[/tex]

[tex]p=13*16[/tex]

[tex]p=208[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{p}{-1}+17=13 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Apply \ the \ properties \ of \ fractions: \frac{a}{-b}=-\frac{a}{b}. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\frac{P}{1} } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Apply\:the\:rule \:\frac{a}{1}=a} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-P} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-P+17=13} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Subtract \ 17 \ from \ both \ sides. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-P+17-17=13-17} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Simplify } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-P=-4} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Divide\:both\:sides\:by\:-1} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{-p}{1}=\frac{-4}{-1} } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Simplify } \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P=4} \end{gathered}$}}[/tex]

What is the value of tan M?
15
15
17
L
∞ ∞01 200
8
17
8
15
15
K 8
8
M

Answers

Answer:

The value of tan M = 15/8

Step-by-step explanation:

[tex]tan \: m \: = \frac{p}{b} \\ tan \: m \: = \frac{15}{8} [/tex]

The diameter of an electric cable is normally distributed, with a mean of 0.9 inch and a standard deviation of 0.02 inch. What is the probability that the diameter will exceed 0.92 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.)

Answers

The probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

What is probability?

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

How to determine the probability?

The given parameters are:

Mean = 0.9

Standard deviation = 0.2

Calculate the z-score at x = 0.92 using

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

z = (0.92 - 0.9)/0.02

Evaluate the numerator; subtract 0.9 from 0.92

z = 0.02/0.02

Divide 0.02 by 0.02. This gives

z = 1

The probability is then represented as:

P(x > 0.92) = P(z > 1)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.92) = 0.841

Hence, the probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

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A stadium has 53,000 seats. Seats sell for $25 in Section A, $20 in Section B, and $15 in Section C. The number of seats in Section A
equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,131,000 from each sold-out event. How many seats
does each section hold?

Answers

The number section A, section B and section C seats sold are 26500, 14200 and 12300 respectively.

How to use equation to find the total number of seat in each section?

The stadium has 53,000 seats.

Seats sell for $25 in Section A, $20 in Section B, and $15 in Section C.

The number of seats in Section A equals the total number of seats in Sections B and C.

Therefore,

a =  b + c

a + b + c = 53000

b + c + b + c = 53000

2b + 2c = 53,000

25a + 20b + 15c = 1131000

25(b + c) + 20b + 15c  = 1131000

25b + 25c + 20b + 15c = 1131000

45b + 40c = 1131000

Hence,

2b + 2c = 53000

45b + 40c = 1131000

40b + 40c  = 1060000

45b + 40c = 1131000

-5b = - 71000

b = - 71000 / -5

b = 14,200

Therefore,

2(14,200) + 2c = 53000

2c = 53000 - 28400

2c = 24600

c = 24600 / 2

c = 12300

Hence,

a =  b + c

a = 14200 + 12300

a = 26500

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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each

Answers

Answer:

a) ∠VUW

b) VY

c) XYV

d) 180°

e) 65°

Step-by-step explanation:

Part A:

A central angle is an angle that creates an arc in a circle, while also having its vertex as the center of the circle.

Here the center is U. So, the vertex of the angle must include U.

This means that there are multiple answers to part a.

The answers can be:

∠VUW

∠WUX

∠XUV

Part B:

A minor arc is any arc that doesn't exceed 180°.

The possible answers for part b, using this definition are:

WV

VY

XY

Part C:

The answer you inputted here is incorrect.

The order of the letters matter.

A tip for you to never mess these up is to trace the letters you've chosen with your finger and see if that image you make with your finger matches up with the shape you wanted to make.

An arc that makes a semicircle is an arc that connects the endpoints of the diameter. The diameter in this case is VX.

This means that your answer must start with V and end with X, or the other way around. (Meaning you could start with x and end with v, but always make sure you keep the endpoints of the diameter as the endpoints of the arc.)

The possible answers for this part are either:

VYX or VWX

Part D:

This arc intercepts the diameter, which is a straight line and a central angle.

The angle of a diameter is 180°.

The arc of an intercepted central angle has the same measure of the central angle itself.

So, the measure of VWX is 180°.

Part E:

If an arc intercepts a central angle, then the arc has the same measure as the central angle.

This rule works the other way around, too.

So, the central angle has the same measure as the minor arc that it intercepts.

Measure of arc VUW is 65°, so m∠VUW is also 65°.

Question 2 of 5
Select the correct answer.
After buying a car, Sarah decides to get it appraised every few years. After owning the car for two years, its value is $5,000. After own
the car for five years, its value is $2,000.
What is the equation that models this inverse variation?
Oy=
O y = 2,500
O
O
5,000
y = 2,000
y =
10,000
Submit
Reset

Answers

The inverse proportional relationship that models this variation is given as follows:

[tex]y = \frac{10,000}{x}[/tex]

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

An inverse proportional relationship is given as follows:

[tex]y = \frac{k}{x}[/tex]

In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:

[tex]y = \frac{k}{x}[/tex]

[tex]5000 = \frac{k}{2}[/tex]

k = 10,000

Hence the relation is:

[tex]y = \frac{10,000}{x}[/tex]

As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.

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A nine year old girl did a science fair experiment in which she tested professional touch therapist to see if they could sense her energy field she flipped a coin to select either her right hand or her left hand and then she asked the therapist to identify the selected hand by placing their hand just under her hand without seeing it and without touching it among 285 trials the touch therapist were correct 116 times use a 0.01 significance level to test the claim that touch therapist use a message equivalent to random guesses to the results suggest that touch therapists are effective

Answers

The test statistic based on the probability illustrated is -3.22.

How to illustrate the probability?

Based on the information, the test statistic will be:

= (0.4 - 0.5)/[✓0.5(1 - 0.5)/260]

= -3.22

The p value using the distribution table is 0.0012.

The conclusion is to reject the null hypothesis as there's sufficient evidence to warrant rejection.

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1/2x + 1/4y = 3 solve for y

Answers

Answer:

y=-2x+12

Step-by-step explanation:

First, subtract 1/2 from each side

1/4y = -1/2x + 3 --> multiply each side by 4

y = -2x + 12 is your final answer

Which inequality is represented by the given graph?
C) y ≤ -3x+6
D) y ≥ 3x+6

Answers

Answer: c, y ≤ -3x+6

Step-by-step explanation:

for example we could use a point on the graph such as (-2, 0)

now we would insert the numbers into the inequality:

y ≤ -3x+6

= 0 ≤ -3(-2) +6

= 0 ≤ 6+6

= 0 ≤ 12

which is true! therefore it is y ≤ -3x+6

16
3. A Ferris wheel with a radius of 25 m makes 2 rotations every minute.
a. State the period of the Ferris wheel.
b. Complete a tables of values showing the height above the ground for 2 rotations of the
Ferris wheel by assigning the correct variables
c. Graph 2 rotations of the Ferris wheel. (Hint: Time Vs Height above the platform)
d. State the amplitude of the Ferris wheel.

Answers

A) The Period is 30 seconds

D) The amplitude is 25 m

How to find the period and amplitude?

A) Since the Ferris wheel makes 2 rotations every minute, then we can say that the period is;

T = 1/2 = 0.5 minutes = 30 seconds

B) Let t be time in seconds and let h be height and as such, we have the formula; h = 25 - 25 cos ((2π/30)t)

Thus, the table is attached showing input values of t and their corresponding h values.

C) The graph of the table above is as attached below.

D) The amplitude is;

Amplitude = (Maximum Point - Minimum Point)/2

Amplitude = (50 - 0)/2

Amplitude = 25

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lim 1 − cos(2x) /x x→0

Answers

The value of the limit of the function given when the value of x tends to zero is 0

What is a limit of a function?

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular inputs.

Given the function limit below;

lim x→0 [1 − cos(2x) /x]

Substitute the value of x into the expression to have;

f(0) = 1-cos2(0)/0
f(0) = 1-1/0

f(0) = 0/0 (ind)

Apply the L'hospital rule to have:

lim x→0 [ − (-2sin2x)) /1]

Substitute the value of x into the result

f(0) = 2sin2(0)/1

f(0) = 2(0)

f(0) = 0

Hence the value of the limit of the function given when the value of x tends to zero is 0

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Find the missing side of the triangle. pythagorean 4 A. 337‾‾‾‾√ km B. 5‾√ km C. 193‾‾‾‾√ km D. 112‾√ km

Answers

The missing side in the given triangle is x = √193 km

Pythagoras theorem

The Pythagoras theorem is expressed as;

x^2 = a^2 + b^2

where

x is the longest side

Substitute the given side

x^2 = 12^2 + 7^2

x^2 = 144 + 49

x = √193 km

Hence the missing side in the given triangle is x = √193 km

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Find the difference between Simple interest and compound interest on 1200 for one year at 10% per annum​

Answers

Answer:

the difference between them is zero cause on first year simple interest and compound interest are equal

Consider the following sample data set of 20 numbers.
24 30 4 42 40 26 23 36 12 45 29 21 34 16 47 28 32 54 19 9
1.
Create a relative frequency table and a frequency histogram with the bin width 8.
2.
Find the sample mean. (Round to the nearest hundredth.)
3.
Find the sample standard deviation

. (Round to the nearest hundredth.)

Answers

The mean = 28.55, while the standard deviation is 13.16

1. The histogram is an attachment

How to calculate for the mean of the data set

We have the following numbers

24 30 4 42 40 26 23 36 12 45 29 21 34 16 47 28 32 54 19 9

The sum of these numbers is given as

571

The total numbers = 20

The mean = 571/20

= 28.55

2 =  How to find the standard deviation

=  (24 - 28.55)2 + ... + (9 - 28.55)/20 - 1

=  3292.95/19

=  173.31315789474

s =  √173.31315789474

=  13.164845532506

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Calculate the perimeter and area of this shape.
Perimeter =
Area =
7.5 cm
6 cm
2 cm
3 cm
2 cm

Answers

area = 25.5 cm²

Step-by-step explanation:

i have shown in the image you have to rotate it to see how i worked the area out

i am very sorry i cant work the perimeter out since i have no idea what the length of the two sides of the triangle are . if you need help on understanding how i worked out the area please let me know .

hopefully i was able to help you in half of the question i am sorry for not helping on the perimeter :)

Answer:

Step-by-step explanation:

Perimeter=25

Which inequality is true when x = 4?

A. X+5<_3

B.x/2<3

c.9x>36

D.18<_-8

Answers


Answer is B. Is true

Which inequality is true when x = 4?

A. X+5<_3

✅B.x/2<3. 4/2 is less than 3 is true!

c.9x>36

D.18<_-8

Answer:

[tex] \sf{b. \frac{x}{2} <3}[/tex]

step by step explanation:

We will try one by one.

A. x + 5 < 3

Step 1. Subtitution Value of x

= 4 + 5 < 3

Step 2. Add by 4 with 5

= 9 < 5

A is wrong because 9 is bigger then 5

B. x/2 < 3

= 4/2 < 3

= 2 < 3

is true because 2 is smaller than 3

C. 9x > 36

9(4) > 36

36 > 36

is wrong, should 36 = 36

D. 18 < 8

is wrong because 18 is bigger than 8

Attached as an image below.

Answers

The formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

Growth constant


The growth constant k can be defined as the frequency or also known as the number of times per unit time of growing by a factor

it is also called the logarithmic return, compounded return, or the force of interest.

Note that the general formula for growth rate is given as;

[tex]P(t) = P0 e^k^t[/tex]

Where,

Po =  Initial value = 400 squirrels

r = Rate of growth

k = constant of proportionality = 0. 5 per year

t = time = 1 year

The function P(t) is given as;

P(t) = 400 e^0.5t

Note that the formula for doubling time is given as;

[tex]TD = t \frac{In 2}{In 1 + r/ 100}[/tex]

r = 4

t = 1

substitute into the formula

[tex]TD = 1 \frac{0. 693}{0. 0392}[/tex]

Doubling time  = 1 × 17. 68

Doubling time = 17. 68 years

Thus, the formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

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50 POINTS!!!!!!!!!!!!!!!!!!!!!!!! SOLVE THIS QUICKLY WITH AN EXPLANATION

Answers

Answer:

x = 22°

Step-by-step explanation:

Between two parallel lines, the opposite inside angles will be congruent. So, x is equal to angle V. The sum of the angles of any triangle will be 180°. Therefore, you can find the value of x by setting all the angles of the triangle SRV equal to 180°.

S = 5x + 4

R = 44

V = x

S + R + V = 180                                         <----- General equation

(5x + 4) + 44 + x = 180                              <----- Insert values

5x + 48 + x = 180                                      <----- Add 4 and 44

6x + 48 = 180                                           <----- Add 5x and x

6x = 132                                                    <----- Subtract 48 from both sides

x = 22                                                      <----- Divide both sides by 6

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