If a storage tank is holding 450 litres when it is three quarters full, how much will it contain when it is two thirds?​

Expansion is the multiplying of each term in the bracket by the expression outside the bracket.  Expansion is also when we multiply to remove the ( ).

How to determine this

Given,

11. [tex](x-8)^{2}[/tex]

By expanding it

= (x-8)(x-8)

Open bracket

= [tex]x^{2} - 8x -8x + 64[/tex]

= [tex]x^{2} - 16x+64[/tex]

Therefore,  [tex](x-8)^{2}[/tex] matches with D. [tex]x^{2} - 16x+64[/tex]

12. (x+6)(x-6)

By expansion

Open bracket

= [tex]x^{2} -6x+6x-36[/tex]

= [tex]x^{2} - 36[/tex]

So, (x+6)(x-6) matches with E. [tex]x^{2} - 36[/tex]

13. (2x-5)(2x+5)

By expanding it

Open bracket

= [tex]4x^{2} +10x -10x-25[/tex]

= [tex]4x^{2} - 25[/tex]

So, (2x-5)(2x+5) matches with H. [tex]4x^{2} - 25[/tex]

14.[tex](3x+1)^{2}[/tex]

Expanding this,

= (3x+1)(3x+1)

Open bracket

= [tex]9x^{2} + 3x +3x+1[/tex]

= [tex]9x^{2} +6x+1[/tex]

Therefore, [tex](3x+1)^{2}[/tex] matches with A. [tex]9x^{2} +6x+1[/tex]

15.[tex](x+4)^{2}[/tex]

By expanding it

= (x+4)(x+4)

Open bracket

= [tex]x^{2} + 4x+4x+16[/tex]

= [tex]x^{2} +8x+16[/tex]

Therefore, [tex](x+4)^{2}[/tex] matches with F. [tex]x^{2} +8x+16[/tex]

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The expression showing the distance is;

100cos30 + 100sin30 ≅ 137 yards. option B

Using the sine identity that is represented as;

sin θ = opposite/hypotenuse

Substitute the values as shown on the diagram, we have that;

sin 30 = y/100

Cross multiply the values, we get;

y= 100(0.5)

Multiply the values

y = 50 yards

Using the cosine identity written as;

cos θ = adjacent/hypotenuse

cos 30 = x/100

cross multiply the values

x = 0.8660(100)

Multiply the values, we get;

x = 86. 6 yards

The total distance = start + end = 86.6 + 50 = 136. 6 yards

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There is not enough evidence to support the claim that older men are shorter than younger men.

The test statistic for this hypothesis test is:

t = (x - μ) / σ / √n

= (69.3 - 69.4) / 2.58 / √119

= -0.13

The p-value for this hypothesis test is:

p-value = P(t < -0.13)

= 0.8944

We cannot conclude that the mean height of older men is less than the mean height of all adult men. The results are not statistically significant.

There is not enough evidence to support the claim that older men are shorter than younger men.

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The age of the watch when David's father lost it was 13. 3 years.

David found the watch 38 years after his father lost it, and the watch worked for 2 years after it was lost. That means the watch was 40 years old when David found it.

When David found it, the watch was 3 times as old as when his father lost it. This means that :

= Number of years lost / 3

= 40 / 3

= 13. 3 years

In conclusion, the watch was 13. 33 years old when David's father lost it.

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The exact value of the trigonometric function by half-angle formula is cos 22.5° = √(2 + √2) / 2. (Correct choice: B)

In this problem we are asked to determine the exact value of a trigonometric function by means of a trigonometric formula known as half-angle formula:

cos 0.5θ = √[(1 + cos θ) / 2]

If we know that θ = 45°, then the exact value of the half-angle formula:

cos 22.5° = √[(1 + cos 45°) / 2]

cos 22.5° = √[(1 + √2 / 2) / 2]

cos 22.5° = √(2 + √2) / 2

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The value of the missing sides in the parallelogram are x = 3 and y = 6

In other to solve the question posted, we use the law which relates to the sides of a parallelogram which establishes that opposite sides of a parallelogram are of equal length.

This means that the side opposite length of 3 will also be 3 and vice-versa

side x = 3

side y = 6

Therefore, the missing sides of the parallelogram are 3 and 6 for sides x and y respectively.

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b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

We also know it took 2 hours Upstream as well as Downstream, and we also know how far it went, so

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&58&b-c&t\\ Downstream&90&b+c&t \end{array}\hspace{5em} \begin{cases} 58=(b-c)(2)\\\\ 90=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{58=(b-c)2}\implies \cfrac{58}{2}=b-c\implies 29=b-c\implies 29+c=b \\\\\\ \stackrel{\textit{using the 2nd equation}}{90=(b+c)2}\implies \cfrac{90}{2}=b+c\implies 45=b+c\implies \stackrel{\textit{substituting}}{45=(29+c)+c} \\\\\\ 45=29+2c\implies 16=2c\implies \cfrac{16}{2}=c\implies \boxed{8=c}~\hfill \stackrel{ 29~~ + ~~8 }{\boxed{b=37}}[/tex]

Answer: Option A) \frac{7}{10} * \frac{5}{8}

Answer:

Graph translated 3 units down

Step-by-step explanation:

Step-by-step explanation:

The exponent you put in the box multiplies the exponent ' 4'    to get the exponent '1'

4 * x = 1

x = 1/4      <====this goes in the box

The probability that Billy gets an orange marble on his first draw and a purple marble on his second draw is P ( A ) = 5/21

Given data ,

To find the probability of Billy drawing an orange marble on his first draw and a purple marble on his second draw, we need to calculate the probability of each event and multiply them together.

Billy's marble jar contains 5 orange marbles and 2 purple marbles. Let's calculate the probabilities for each draw:

Probability of drawing an orange marble on the first draw:

Billy has a total of 5 + 2 = 7 marbles in the jar.

The probability of drawing an orange marble on the first draw is 5/7 since there are 5 orange marbles out of the total 7 marbles.

Probability of drawing a purple marble on the second draw:

After the first draw, there will be 6 marbles left in the jar, with 4 orange marbles and 2 purple marbles remaining.

The probability of drawing a purple marble on the second draw is 2/6 since there are 2 purple marbles out of the remaining 6 marbles.

Probability = (5/7) * (2/6)

Probability = 10/42

Probability = 5/21

Hence , the probability that Billy gets an orange marble on his first draw and a purple marble on his second draw is 5/21

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Answer:

A. 3x+12

Step-by-step explanation:

8x+3-5x+9

8x-5x=3x

3+9=12

then put them together

3x+12

answer= A

The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.

The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.

In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.

The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.

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The number of adults who paid for the ticket are 170 adults and the number of children who paid for the ticket are 80 children.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of children tickets sold, and then translate the word problem into an algebraic equation as follows:

Since 250 people attended the game, a linear equation that models the situation is given by:

x + y = 250     ....equation 1.

Additionally, adult tickets sold for $100 while children tickets sold for $50 each with a total revenue was $21,000, a linear equation that models the situation is given by:

100x + 50y = 21,000   .......equation 2.

By using the substitution method to solve the equations simultaneously, we have:

100x + 50(250 - x) = 21,000

100x + 12,500 - 50x = 21,000

50x = 21,000 - 12,500

x = 8,500/50

x = 170 adults.

For the children tickets sold, we have:

y = 250 - x

y = 250 - 170

y = 80 children.

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Complete Question:

Attendance at a game was 250 people, the admission ticket for an adult was $100 and for children $50, if the collection was $21,000, how many adults and how many children paid for the ticket?

By Using

[tex] \sf \: Exterior \:Angle\: Property \:of\: triangle[/tex]

[tex] \large \sf \: → x = 67° + 90° [/tex]

[tex] \large \bf \: → x = 157° [/tex]

[tex] \underline{ \rule{200pt}{6pt}}[/tex]

Answer: 5(f+7)

Step-by-step explanation: I know you didn't ask for an explanation but here:

First what you want to do is find what both terms have in common, the LCM, (least common multiple), is the only thing common between them, which is 5, so divide 35 by 5, which is 7, and since you divided by 5, you put it outside, and put f and 7 together.

Answer:

Problem 9:  One solution

Problem 10:  Infinitely many solutions

Problem 11: One solution

Problem 12:  No solution

Step-by-step explanation:

Solving one-variable equations

When solving a one variable equation, there are two steps:

During Step 1 of that process, usually one will be combining like-terms to take two terms that contain x, and merging them into one term that contains x.  However, occasionally, the like terms contain x will completely cancel, leaving an equation with no variable left in it.

At that point, there are one of two possibilities:

If the remaining equation is true, it doesn't matter what the value of x is, the equation will be true.  This means there are infinitely many solutions (any value of x will make the equation true).

Similarly, if the remaining equation is false, it doesn't matter what the value of x is, the equation will be false.  This means there are no solutions (no values of x that will make the equation true).

Problem 9

[tex]3-x=x-3[/tex]

Add "x" to both sides to move the x-term on the left side of the equation from the left, to the right side, and group like terms.

[tex]3=2x-3[/tex]

We were able to combine like terms containing the x into a single term.  This equation will have one solution.

The remaining work is unnecessary to answer the question, but shows that there is one solution, the steps to find it, and what it is.

[tex]6=2x[/tex]

[tex]3=x[/tex]

Problem 10

[tex]4x-8=4(x-2)[/tex]

Use the distributive property on the expression on right hand side of the equation ...

[tex]4x-8=4x-8[/tex]

Observe that at this point, the entire left hand side of the equation EXACTLY matches that of the entire right hand side of the equation.

They are not just equal, they are exactly the same.

Attempting to move the term with x on the left hand side to the right hand side will require subtracting 4x from both sides, but combining like terms will cancel all terms with x on both sides....

[tex]-8=-8[/tex]

Since negative eight is ALWAYS equal to negative eight, no matter what value you choose for x, the equation must be true because each side is the same exact expression.  This means there are infinitely many solutions.

Problem 11

[tex]5(1-x)=5+5x[/tex]

Apply the distributive property on the expression on left hand side of the equation ...

[tex]5-5x=5+5x[/tex]

Add 5x to both sides of the equation to move the terms with x on the left side to the right side of the equation, and combine like terms...

[tex]5=5+10x[/tex]

Again, we were able to combine like terms containing the x into a single term.  This equation will have only one solution:

Subtract 5 from both sides...

[tex]0=10x[/tex]

Divide both sides by 10...

[tex]0=x[/tex]

Problem 12

[tex]x+2(x-7)=3x-7[/tex]

Apply the distributive property on the expression on left hand side of the equation ...

[tex]x+2x-14=3x-7[/tex]

Combine like terms on the left hand side of the equation...

[tex]3x-14=3x-7[/tex]

To move the term with x from the left side to the right side, subtract 3x from both sides, and combine like terms...

[tex]-14=-7[/tex]

Here, when combining like terms, the x all canceled out, and negative 14 is not equal to negative 7.  So, there is no solution so this equation.

The area of triangle DEF is four times larger than the area of triangle ABC.

We have,

Right triangle ABC was dilated with a scale factor of 2.

When a triangle is dilated with a scale factor of 2, the resulting triangle is enlarged by a factor of 2 in each dimension.

Since area is a two-dimensional measure, it will be enlarged by a factor of the square of the scale factor.

In this case, the scale factor is 2, so the area of triangle DEF will be

=  2²

= 4 times larger than the area of triangle ABC.

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Answer:

1. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x

2. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x

4. To predict how many shares each student's post will be received on Day 3 and Day 10, substitute the respective values of x into each function:

a) On Day 3, Amber's post will have f(3) = 3(4)^3 = 192 shares. On Day 10, Amber's post will have f(10) = 3(4)^10 = 6,291,456 shares.

b) On Day 3, Ben's post will have f(3) = 2(3)^3 = 54 shares. On Day 10, Ben's post will have f(10) = 2(3)^10 = 196,830 shares.

c) On Day 3, Carter's post will have f(3) = 10(2)^3 = 80 shares. On Day 10, Carter's post will have f(10) = 10(2)^10 = 10240 shares.

5. The graph of Amber's post with copies mailed to the assisted living facility will have the same shape and growth rate as the original function, but it will be shifted upwards by 45 units along the y-axis.

6. Ben's post travels the fastest because it has the largest growth rate of 3 (compared to Amber's 4 and Carter's 2), meaning it triples every day.

7. It depends on the specific purpose of the post. If the goal is to have a widespread influence and viral impact, then Amber's approach of starting with a smaller group of initial shares but a higher growth rate might be more effective. On the other hand, if the goal is to create a more tight-knit network of shares with a smaller number of initial friends, then Carter's approach might be more appropriate.

Cody will paint a total of 800 square centimeters.

1. Determine the dimensions of the rectangular prism:

  Length = 20 cm

  Width = 12 cm

  Height = 10 cm

2. Calculate the surface area of each face of the rectangular prism:

  Front and back faces: Length × Height = 20 cm × 10 cm = 200 cm² each

  Top and bottom faces: Width × Length = 12 cm × 20 cm = 240 cm² each

  Side faces: Height × Width = 10 cm × 12 cm = 120 cm² each

3. Add up the surface areas of all the faces:

  Front and back: 200 cm² + 200 cm² = 400 cm²

  Top and bottom: 240 cm² + 240 cm² = 480 cm²

  Sides: 120 cm² + 120 cm² = 240 cm²

4. Calculate the total surface area by summing up all the face areas:

  Total surface area = Front and back + Top and bottom + Sides

  Total surface area = 400 cm² + 480 cm² + 240 cm² = 1120 cm²

5. However, since Cody is only painting the surfaces, excluding the interior of the box, the total surface area to be painted would be half of the total surface area calculated above.

6. Calculate the final painted surface area:

  Final painted surface area = Total surface area / 2

  Final painted surface area = 1120 cm² / 2 = 560 cm²

Therefore, Cody will paint a total of 560 square centimeters.

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If  sin 60° = √3/2 then it follows that Cos 30 = √3/2

Through precise geometric connections found inside a right triangle, the trigonometric ratios of 60 degrees and 30 degrees are connected. These relationships arise due to the specific geometric properties and angles of the right triangle and are frequently linked to the unique angles of 30, 45, and 60 degrees.

Given that;

Sin(30°) = 1/2

Sin(60°) = √3/2

Then;

Cos(30°) = √3/2

Cos(60°) = 1/2

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Answer:

-5, x=2

Step-by-step explanation:

name me brainliest and say thank you and please verify.

The value of function g(1) is 45, g(0.1) is 22.23, and g(0.01) is 20.22.

To determine the values of g(1), g(0.1), and g(0.01), we need to substitute the given values into the expression for g(h) and evaluate their function them.

First, let's find the expression for g(h):

[tex]g(h) = \frac{(f(3 + h) - f(3))}h[/tex]

Now, substitute the function f(x) into g(h):

[tex]g(h) = \frac{((3(3 + h)^2 + 4(3 + h) + 5) - (3(3)^2 + 4(3) + 5))}h[/tex]

Simplifying further:

[tex]g(h) = \fract{((3(9 + 6h + h^2) + 12 + 4h + 5) - (27 + 12 + 5))}{h}\\\\g(h) = \frac{(27 + 18h + 3h^2 + 12 + 4h + 5 - 27 - 12 - 5)}h\\\\g(h) = \frac{(3h^2 + 22h + 20)}h[/tex]

Now, we can substitute the values of h into the expression to find g(1), g(0.1), and g(0.01):

[tex]g(1) =\frac{ (3(1)^2 + 22(1) + 20)}1 = 3 + 22 + 20 = 45\\\\g(0.1) = \frac{(3(0.1)^2 + 22(0.1) + 20)}{0.1} = 0.03 + 2.2 + 20 = 22.23\\\\g(0.01) = \frac{(3(0.01)^2 + 22(0.01) + 20)}{0.01} = 0.0003 + 0.22 + 20 = 20.22[/tex]

Therefore, the value of function g(1) is 45, g(0.1) is 22.23, and g(0.01) is 20.22.

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Answer:

1191 cm²

Step-by-step explanation:

Area of parallelogram = base X vertical height.

Call the vertical line h.

h/ sin 80  =  7/ sin 10

h = (7 sin 80) / sin 10

= 39.7.

Area of parallelogram = 30 X 39.7

= 1191 cm²

The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.

Given:

Side length = 30 cm

Using Trigonometry

tan 80 = P / Base

5.6712 = P / 7

P = 39.6984 cm

Using the formula for Area of parallelogram

= Base x height

= 30 x 39.6984

= 1,190.952 square cm.

Therefore, the area is 1,190.952 square cm.

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The solution of inequality is shown in image.

We have to given that;

Inequality is,

⇒ - 4/5 - 9.2w < 1.24w - 3.75

Now, We can simplify as;

⇒ - 4/5 - 9.2w < 1.24w - 3.75

Add 3.75 both side,

⇒ - 4/5 - 9.2w + 3.75 < 1.24w - 3.75 + 3.75

⇒ - 0.8 - 9.2w + 3.75< 1.24w

Add 9.2w both side,

⇒ 2.95 < 1.24w + 9.2w

⇒ 2.95 <  10.44w

⇒ 0.3 < w

Hence, The solution of inequality is shown in image.

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The fuel efficiency of the first car is 35 miles per gallon, and the fuel efficiency of the second car is 40 miles per gallon.

Let's assume the fuel efficiency of the first car is x miles per gallon and the fuel efficiency of the second car is y miles per gallon.

Given that the first car consumed 15 gallons of gas and the second car consumed 25 gallons, we can set up the following equations:

15x + 25y = 1525 -- (Equation 1) (Total miles driven by both cars)

x + y = 75 -- (Equation 2) (Sum of their fuel efficiencies)

To solve this system of equations, we can use substitution or elimination method. Let's solve it using the substitution method:

From Equation 2, we can express y in terms of x:

y = 75 - x

Substituting this value of y into Equation 1:

15x + 25(75 - x) = 1525

Expanding and simplifying:

15x + 1875 - 25x = 1525

-10x = -350

Dividing both sides by -10:

x = 35

Substituting the value of x back into Equation 2 to find y:

y = 75 - x

y = 75 - 35

y = 40

Therefore, the fuel efficiency of the first car is 35 miles per gallon, and the fuel efficiency of the second car is 40 miles per gallon.

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The equation of the regression line is approximately:

y = -5.347x + 24.405

To find the equation of the regression line, we need to perform linear regression on the given data points.

The equation of a regression line is typically represented as:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

In this case, the independent variable is the family income (x) and the dependent variable is the ulcer rate (y).

We can calculate the slope (m) and y-intercept (b) using the following formulas:

m = (Σ(xy) - (Σx)(Σy) / n(Σx²) - (Σx)²)

b = (Σy - m(Σx)) / n

Let's calculate the slope (m) and y-intercept (b) using the given data points:

Income (x)                                        Ulcer rate (y)

4000                                                    12.9

6000                                                    12.8

8000                                                    12.4

12000                                                   11.9

16000                                                   12.3

20000                                                   11.1

30000                                                   10.5

45000                                                    8.5

60000                                                   7.2

Σx = 4000 + 6000 + 8000 + 12000 + 16000 + 20000 + 30000 + 45000 + 60000 = 224000

Σy = 12.9 + 12.8 + 12.4 + 11.9 + 12.3 + 11.1 + 10.5 + 8.5 + 7.2 = 100.6

Σxy = (4000 * 12.9) + (6000 * 12.8) + (8000 * 12.4) + (12000 * 11.9) + (16000 * 12.3) + (20000 * 11.1) + (30000 * 10.5) + (45000 * 8.5) + (60000 * 7.2) = 2,685,000

Σx² = (4000²) + (6000²) + (8000²) + (12000²) + (16000²) + (20000²) + (30000²) + (45000²) + (60000²) = 8,144,000,000

n = 9 (number of data points)

Now, let's substitute these values into the formulas to find m and b:

m = (Σ(xy) - (Σx)(Σy) / n(Σx²) - (Σx)²)

= (2,685,000 - (224000 * 100.6) / (9 * 8,144,000,000) - (224000)²

≈ -5.347

b = (Σy - m(Σx)) / n

= (100.6 - (-5.347) * 224000) / 9

≈ 24.405

Therefore, the equation of the regression line is approximately:

y = -5.347x + 24.405

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The values of real numbers a, b, and c are,

a = 3/4

b = - 1/4

c = 3

Since, We have to given that;

The graph of the function y = ax² + bx + c contains the points (-1,4), (3,9) and (0,3).

Now, We can formulate;

The points are satisfy the function.

So, We get;

y = ax² + bx + c

Put x = - 1, y = 4

4 = a (- 1)² + b (- 1) + c

4 = a - b + c  ... (i)

y = ax² + bx + c

Put x = 3, y = 9

9 = a (3)² + b (3) + c

9 = 9a + 3b + c  .. (ii)

y = ax² + bx + c

Put x = 0, y = 3

3 = a (0)² + b (0) + c

3 = c   .. (iii)

In equation (i) put c = 3;

4 = a - b + c

4 = a - b + 3

a - b = 4 - 3

a - b = 1   .. (iv)

In equation (ii) put c = 3;

9 = 9a + 3b + c

9 = 9a + 3b + 3

9a + 3b = 6

3a + b = 2  . (v)

Add (iv) and (v);

4a = 3

a = 3/4

And, a - b = 1

3/4 - b = 1

3/4 - 1 = b

b = - 1/4

Hence, The values of a, b, and c are,

a = 3/4

b = - 1/4

c = 3

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Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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Answer: The equation of the circle can be rewritten in standard form by completing the square for both x and y terms. The standard form of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

17 + y^2 + 6x = 6y + 63 y^2 - 6y + 6x + 17 = 63 y^2 - 6y + 9 + 6x = 63 + 9 (y - 3)^2 + 6x = 72 (y - 3)^2 + 6(x - (-6)) = 72 (y - 3)^2 + (x + 6)^2 = 72

From this we can see that the center of the circle is (-6,3) and the radius is sqrt(72) = 6sqrt(2).

I’m sorry but I’m unable to draw a graph for you.