An square aquarium which is 15cm long has 1250 millilitres of water how much more water needed to fill the aquarium completely

Answer:

3x + 5 = 4x - 40

x = 45

5y - 50 = y

4y = 50

y = 25/2

The opening of the pail has a diameter of approximately 55.4 inches (since it's twice the diameter of the base).

Based on the information you provided, it sounds like you have some great supplies for making sand castles at the beach with your friends.

Firstly, let's take a look at the pail. You mentioned that it has a base with a circumference of 87 inches, which means that the diameter of the base is approximately 27.7 inches (since circumference = pi x diameter). The pail is also 12 inches tall and has an opening on top that is twice the diameter of the base. Therefore, the opening has a diameter of approximately 55.4 inches (since it's twice the diameter of the base). With these measurements, you can use the pail to make some pretty big sand castles!

Next, you mentioned a plastic pyramid mold that has a square base with an edge that measures 6 inches and is 7 inches tall. This mold should be perfect for making pyramid-shaped sand castles. Just fill it with sand, pack it down, and carefully remove the mold to reveal your pyramid!

Finally, you mentioned an empty soup can with a diameter of 5.25 inches and is 6.5 inches tall. This can could be used to make cylindrical shapes in your sand castles. Simply pack sand around the can, press down firmly, and carefully remove the can to reveal your cylinder.

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Answer: y = 1.4

Step-by-step explanation:

if you write the equation it would be

-5y - 4 = -11

so first you would subtract 4 from -4 and -11 to cancel out the four.

so your equation would look like this -5y= -7

so now u would divide -5 by both sides to canceled out the -5

your equation should end up looking like

y=1.4

The point where line A intersects line B is [2, 10].

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (1, 10 1/3) and a slope of -1/3, a linear equation for this line can be calculated or determined by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 10 1/3 = -1/3(x - 1)

y - 31/3 = -x/3 + 1/3

For Line B, we have:

y - y₁ = m(x - x₁)

y - (-2) = 1/3(x - (-34))

y + 2 = x/3 + 34/3

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The distance where the ladder is touching the building for triangle 2 is 12 ft

From the question, we have the following parameters that can be used in our computation:

Ladder 1

Distance along the ground = 12 ft

Distance touching the ladder = 8 ft

Ladder 2

Distance along the ground = 18 ft

Distance touching the ladder = x

Using proportion of similar triangles, we have

x : 18 = 8 : 12

Express as fraction

x/18 = 8/12

So, we have

x = 18 * 8/12

Evaluate

x = 12

Hence, the distance where the ladder is touching the building for triangle 2 is 12 ft

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Answer:

12?

Step-by-step explanation:

Not too sure! I am in the middle of taking the test right now though

The integral ∫(5/5)dx/√[86(x^2 - x^2)] converges to 5 since the denominator becomes 0 at x=0, which is not in the interval of integration [5,5].

We can start by simplifying the integrand

∫(5/5)dx/√[86(x^2 - x^2)]

Using the identity a^2 - b^2 = (a + b)(a - b), we can rewrite the denominator as

√[86(x^2 - x^2)] = √[86(x + x)(x - x)] = √[86] * √[x + x] * √[x - x] = √[86] * √[2x] * √[0] = 0

Therefore, the integrand is undefined when x = 0. Since the interval of integration is [5,5], which does not include 0, the integral is well-defined and converges to 5.

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first off, let's look at the equation of the circle

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{}{h}~~,~~\underset{}{k})}\qquad \stackrel{radius}{\underset{}{r}} \\\\[-0.35em] ~\dotfill\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})=169\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})=\stackrel{ r }{13^2}[/tex]

so we have a circle centered at (3 , 7) with a radius of 13, Check the picture below.

so the line we want is the line in purple, which is tangential to the circle and therefore perpendicular to the blue line.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the blue line

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{3}}} \implies \cfrac{ -5 }{ 12 } \implies - \cfrac{5 }{ 12 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-5}{12}} ~\hfill \stackrel{reciprocal}{\cfrac{12}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{12}{-5} \implies \cfrac{12}{ 5 }}}[/tex]

so we're really looking for the equation of a line whose slope is 12/5 and it passes through (15 , 2)

[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{12}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{12}{5}}(x-\stackrel{x_1}{15}) \\\\\\ y-2=\cfrac{12}{5}x-36\implies {\Large \begin{array}{llll} y=\cfrac{12}{5}x-34 \end{array}}[/tex]

Answer:

f¹(12) = 20

Step-by-step explanation:

f(-2) = 24

f(-1) = 17

f(0) = 12

f(1) = 9

f¹(x) = 2x - 4

f¹(12) = 20

Answer:

p=3

Step-by-step explanation:

To determine if two lines intersect, compare their slopes and y-intercepts, and solve their equations simultaneously.

To determine if two lines intersect, you need to compare their key features, such as their slope and y-intercept.

If the slopes of the two lines are different, then they will intersect at some point.

If the slopes are the same, then the lines may or may not intersect, depending on whether or not their y-intercepts are also the same.

To find the point of intersection, you can set the two linear functions equal to each other and solve for the variable. The resulting value will give you the x-coordinate of the intersection point, which can then be substituted back into either equation to find the corresponding y-coordinate.

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The linear equation from the given scatterplot will be y = -0.1x + 9.

On the given scatterplot we have the song released details on the x-axis and the average rating of the songs by the family members on the y-axis.

To get the linear equation from the given scatterplot we have to find the y-intercept of the equation.

The general form of the equation is y = mx + c

here, m is the slope and c is the y-intercept.

By, the given graph we can say that y is intercepting at the value '9'. So, the y-intercept is 9.

To find the slope we have to take two points,

Let's take two points as (1970, 7) and (1990, 5).

From the points slope = (5-7)/(1990-1970)

                                     = -2/20 = -1/10 = -0.1

So, the equation from the given scatterplot is y = mx+c

So, y = -0.1x + 9.

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Answer:

The Answer is 5

Step-by-step explanation:

Pink beads : White beads

30 : 35

( 30 / 5 ) : ( 35 / 5 )

6 : 7

To find the number of beads, You divide the number of pink beads available by the number of pink beads in the ratio:

= 30 / 6

= 5 necklaces

hope this helps :)

Answer:

y = 9

Step-by-step explanation:

• Parallel lines have equal slopes

calculate the slope m of  TU using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = T(- 7, 4 ) and (x₂, y₂ ) = U(- 2, - 6 )

[tex]m_{TU}[/tex] = [tex]\frac{-6-4}{-2-(-7)}[/tex] = [tex]\frac{-10}{-2+7}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2

now calculate the slope of VW and equate to - 2

with (x₁, y₁ ) = V(8, 7 ) and (x₂, y₂ ) = W(7, y )

[tex]m_{VW}[/tex] = [tex]\frac{y-7}{7-8}[/tex] = [tex]\frac{y-7}{-1}[/tex]

now equating gives

[tex]\frac{y-7}{-1}[/tex] = - 2 ( multiply both sides by - 1 to clear the fraction )

y - 7 = 2 ( add 7 to both sides )

y = 9

The total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.

The marginal cost function for producing the x-th item of a certain brand of bar stool is given by MC(x) = 20 - 0.5x, where 0 ≤ x ≤ 100. To estimate the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles, we first need to calculate the width of each rectangle.

The width of each rectangle is (100 - 0) / 5 = 20.

Now, we will evaluate the marginal cost function at the left endpoints of each rectangle:
MC(0) = 20 - 0.5(0) = 20
MC(20) = 20 - 0.5(20) = 10
MC(40) = 20 - 0.5(40) = 0
MC(60) = 20 - 0.5(60) = -10
MC(80) = 20 - 0.5(80) = -20

Next, multiply each value by the width (20) and sum the results to approximate the variable cost:
Variable cost ≈ 20(20) + 10(20) + 0(20) + (-10)(20) + (-20)(20) = 400 + 200 - 200 - 400 = 0

Finally, add the fixed cost of $200 to the variable cost:
Total cost ≈ $200 + $0 = $200

So, the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.

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270 students in a seventh-grade class of 450 would have a cell phone which denotes three-fifths of seventh graders using fractions.

Total number of students = 450

Percent of students who have cell phones = 3/5 th

In a class, if there are three-fifths of students have cell phones, that means we need to calculate the remaining percent of students who did not have cell phones.

Students without cell phones = 1 - 3/5 = 2/5

The total number of students with cell phones = (3/5) x 450

The total number of students with cell phones = 270

Therefore, we can conlcude that 270 students in a seventh-grade class of 450 would have a cell phone.

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Answer:

AEC is similar to BDC in terms of the type of triangle

That's all I can really say

I hope this helps :)

In ΔMNO, possible values of ∠N are 64.6° and 115.4°.

To find the possible values of ∠N, follow these steps:

1. Since the sum of angles in a triangle is 180°, we first find ∠O by subtracting ∠M from 180°: 180° - 38° = 142°.

2. Next, we use the Law of Sines to find the sine of ∠N: sin(∠N) = (n * sin(∠O)) / m = (88 * sin(142°)) / 60.

3. Solve for sin(∠N), which gives us two possible values: sin(∠N) ≈ 0.8988 and sin(∠N) ≈ -0.8988.

4. Find the inverse sine (arcsin) of both values to get the possible angles for ∠N: arcsin(0.8988) ≈ 64.6° and arcsin(-0.8988) ≈ 115.4° (adding 180° to the negative result).

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The area of the lawn that is watered by the sprinkler is approximately 200.96 square feet.

The area of the field that's  doused  by the sprinkler is a sector of a circle with a compass of 8  bases and a central angle of 360 degrees.

To find the area of the sector, we can use the formula

Area = ( θ/ 360) x πr2

 where θ is the central angle in degrees,

r is the radius of the circle,

and π is the constant pi.  

Substituting the given values,

we get   Area = (360/360) x3.14 x 82

Area = 3.14 x 64  Area = 200.96

Thus, the area of the field that's  doused  by the sprinkler is  roughly 200.96 square feet.

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The complete question is as follows:

Michael is using a rotating sprinkler to water his lawn. The sprinkler rotates in a complete circle. It sprays water at most 8 feet. Find the area of the lawn that is watered.

The distance from P to the airplane is y = x + 100 ≈ 628.38 m.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

From a certain point Q on a straight road, which forms an angle of 22° with the horizontal, the angle of elevation of an airplane at point A is 57°. At the same instant from another point Q, 100 meters ahead of the first point, the angle of elevation of the airplane is 63°. The points P, Q, and A are in the same vertical plane. Find the distance from P to the airplane.

To solve the problem, we can use the concept of similar triangles. Let's call H the height of the airplane and x the distance from Q to the airplane. Then, the distance from P to the airplane is given by y = x + 100.

From triangle QA1H, we have:

tan(57°) = H / x

From triangle QA2H, we have:

tan(63°) = H / (x + 100)

Dividing these two equations, we get:

tan(57°) / tan(63°) = x / (x + 100)

Solving for x, we get:

x = 100 * tan(63°) / (tan(63°) - tan(57°)) ≈ 528.38 m

Therefore, the distance from P to the airplane is:

y = x + 100 ≈ 628.38 m.

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Answer:

2.2

Step-by-step explanation:

To find your GPA, use the attached image:

After you've written down your numerical scores, divide it by the total classes you're taking, which is 7.

So, your GPA is 2.2

Answer:

y-3x-2

Step-by-step explanation:

take 2 points (1,1), (3,7)

find the slope: 7-1/3-1=3

plug into y=2x+b (used pt (1,1) )

1=3(1)+b

1=3+b

b=-2

y=3x-2

Answer:

Problem 8:
Option C)       DE = √21

Problem 9:
Option C)     Perimeter = 30 cm

Step-by-step explanation:

1. Problem 8

Draw a line segment connecting the center of the circle, X, to A. This is the radius of the circle

The points ABX form a right triangle with AX as the hypotenuse and AB, BX as the legs of the right triangle

By the Pythagorean theorem
hypotenuse² = sum of the squares of the two legs

Plugging in line segment references

AX² = AB² + BX²

We are given AC = 8, BX = 3

Since the segment BX intersects AC at right angles, AB = BC = AC/2

So AB = 8/2= 4

Plugging these values into the Pythagorean formula
AX² = AB² + BX²

AX² = 4² +3²

AX² = 16 + 9

AX² = 25

Draw a line connecting X and D
The points DEX form a right triangle with DX as the hypotenuse and EX and DE as the legs

Again, by the Pythagorean theorem

DX² = DE² + EX²

But DX is the radius of the circle so it must be the same as AX

Substitute for DX in terms of AX
DX² = DE² + EX²

=> AX² = DE² + EX²

But AX² = 25 and EX = 2 giving EX² = 4

Therefore

AX² = DE² + EX² becomes
25 = DE² + 4

DE² = 25 - 4

DE² = 21

DE = √21

This is choice C

Problem 9

To find the perimeter, just add up the individual side lengths:

Perimeter = 10 + 8 + 7 + 5 = 30 cm

Option C

Answer:

Its 12

Step-by-step explanation:

1.   Following PEMDAS, we first solve the equation inside the parentheses.

       -4(-2) = 8

       -12 ÷ 3 = -4

       -20 + 4 = -16

2.    Now, we have the following expression:

       8 + (-4) + (-16)

 3.  Again, following PEMDAS, we solve the equation inside the parentheses first.

       8 + (-4) + (-16) = 8 - 4 - 16

  4. Finally, we solve the equation from left to right.

       8 - 4 - 16 = 8 - (4 + 16)

       8 - (20) = -12

Therefore, the value of the expression is -12.

To find the relative frequency of boys who want to go to the water park, we need to divide the number of boys who want to go to the water park by the total number of boys in the sample:

Relative frequency = Number of boys who want to go to the water park / Total number of boys

Assuming you have the necessary data, you can compute this value by dividing the number of boys who want to go to the water park by the total number of boys and rounding the result to the nearest hundredth.

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a) The quantity (in hundreds of units) that will give maximum profit: [tex]x^{2}[/tex] + 6x - 3022 = 0

b) The maximum profit is approximately $202,573.42.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

(a) To find the quantity that will give maximum profit, we need to find the level of output at which marginal revenue equals marginal cost.

The total revenue function for the monopoly is TR = px, where p is the price and x is the quantity sold. The marginal revenue is the derivative of the total revenue with respect to x, which is MR = d(TR)÷dx = p + x(dp÷dx).

To find the marginal revenue function, we differentiate the demand function with respect to x:

dp÷dx = -(2÷3)x

So, the marginal revenue function is:

MR = (2104 - (1÷3)[tex]x^{2}[/tex]) - (2÷3)[tex]x^{2}[/tex]

To find the marginal cost function, we differentiate the average cost function with respect to x:

dC÷dx = 22 + 2x

So, the marginal cost function is:

MC = 22 + 2x

To find the level of output at which MR = MC, we set the two functions equal to each other:

(2104 - (1÷3)[tex]x^{2}[/tex]) - (2÷3)[tex]x^{2}[/tex] = 22 + 2x

Simplifying this equation, we get:

[tex]x^{2}[/tex] + 6x - 3022 = 0

(b) Using the quadratic formula, we find that:

x = (-6 ± √( 36- 4(1)(-3022))) / 2(1)

x = (-6 ± √(36444)) / 2

x = (-6 ± 190.81) ÷ 2

x ≈ -98.4 or x ≈ 92.4

Since we can't produce a negative quantity, we choose x ≈ 92.4 as the quantity that will give maximum profit.

Therefore, the level of output that will maximize profit is 924 units (in hundreds of units).

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The graph of the function will touch the x-axis at x = -5, but not cross it, and the behavior of the graph near x = -5 will be determined by the degree of the zero (which is 3 in this case).

The polynomial function that represents the volume of a sphere with radius x+5 is given by:

[tex]V(x) = (4/3)\pi (x+5)^3[/tex]

To find the multiplicity of the zero, we need to factor out the (x+5) term from the polynomial:

V(x) = (4/3)π(x+5)(x+5)(x+5)

We can see that the zero is x = -5, and it has a multiplicity of 3, since there are three factors of (x+5) in the polynomial.

This means that the graph of the function will touch the x-axis at x = -5, but not cross it, and the behavior of the graph near x = -5 will be determined by the degree of the zero (which is 3 in this case).

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The solution to the equation √8x + 4 = 6 is x = 0.5.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the equation in the question:

√8x + 4 = 6

To solve for x in the equation, isolate the term containing the variable x.

Subtract 4 from both sides of the equation:

√8x + 4 - 4 = 6 - 4

√8x = 6 - 4

√8x = 2

Square both sides of the equation:

( √8x )² = 2²

8x = 4

Divide both sides of the equation by 8:

x = 4/8

x = 1/2

x = 0.5

Therefore, the value of x is 0.5.

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The correct answer is: c. null: mu1 - mu2 = 0; alternative: mu1 - mu2 is not equal to 0

The null hypothesis states that there is no significant difference in the mean lifespan of people in the two towns, while the alternative hypothesis states that there is a significant difference in the mean lifespan of people in the two towns.

Since we are comparing the means of two populations, we use the difference between the means as the test statistic. Therefore, the null hypothesis is mu1 - mu2 = 0 (there is no difference between the means) and the alternative hypothesis is mu1 - mu2 is not equal to 0 (there is a difference between the means).

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