A basin can hold 8542ml of water.the basin can hold 0.458l more water than a fish tank. how much water can the fish tank hold?express your answer in litres.

Assuming Boden does not add or take out any money, he would have $470.4 in the account after 4​ years.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 400 × 4.4/100 × 4

S.I = 400 × 0.044 × 4

S.I = $70.4.

Next, we would calculate the future value as follows;

S.I = A - P

Future value, A = S.I + P

Future value, A = $70.4 + $400

Future value, A = $470.4.

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Answer:

He makes $123.48 a week

Answer:

x=15

Step-by-step explanation:

[tex]\angle A+\angle B+\angle C=180^\circ\\(5x-27)^\circ+(7x-26)^\circ+[180^\circ-(10x-23)^\circ]=180^\circ\\12x-53+180-10x+23=180\\2x-30+180=180\\2x-30=0\\2x=30\\x=15[/tex]

Answer:

x = 15.

Step-by-step explanation:

By the External angle of a triangle theorem:-

The external angle = the sum of the 2 opposite internal angles.

So:

10x - 23 = 7x - 26 + 5x - 27

10x - 7x - 5x = -27 - 26 + 23

-2x = -30

x = 15.

Answer:

4:8=1:2

3:9=1:3

10:2=5

3:18 is the same thing as 3:18

Answer:

C

Step-by-step explanation:

The graph passes through [tex](-2,-5)[/tex] but not [tex](2,5)[/tex].

The line is steep, and has a slope of more than 1.

The percent of the bug eaten each day is 67% and the percent of the bug remaining each day is 33%.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

f(x) = 500 (0.67)ˣ

Part A :

x = 0 ⇒ f(x) = 500 (0.67)⁰ = 500

x = 1 ⇒ f(x) = 500 (0.67)¹ = 335

x = 2 ⇒ f(x) = 500 (0.67)² = 224.45

x = 3 ⇒ f(x) = 500 (0.67)³ = 150.3815

Part B :

Here 0.67 is the decay rate.

That is the rate of decay of the bug is 0.67.

67% of the bugs are decaying with each day.

Part C :

Percent of bugs remaining each day = 100% - 67% = 33%

Part D:

f(x) < 40

500 (0.67)ˣ < 40

(0.67)ˣ < 40 / 500

(0.67)ˣ < 0.08

Taking logarithms on both sides,

㏒ (0.67)ˣ < ㏒ 0.08

x ㏒ (0.67) < ㏒ 0.08

x (-0.1739) < (-1.0969)

Dividing doth sides by (-0.1739), the sign of inequality changes because of dividing by a negative number.

x > 6.3

Hence the percentage of the bugs eaten and remained are calculated.

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[tex](4x - 8) - (3x + 10)[/tex]

Distribute negative sign:

[tex]4x-8+-1(3x)+(-1)(10)[/tex]

[tex]4x-8-3x-10[/tex]

Combine Like Terms:

[tex](4x-3x)+(-8-10)[/tex]

[tex]=\fbox{x - 18}[/tex]

Answer:

[tex]x - 18[/tex]

[tex]4x - 8 - 3x - 10 \\ 4x - 3x - 8 \times 10 \\ x - 18[/tex]

Aiden run and walk in 60 ​minute, then the distance = 9180 meters

Given that,

Aiden run at a constant peed of 3. 5 meter per second for 1/2 hour.

Then, he walk at a rate of 1. 6 meter per second for 1/2 hour.

(1) 3. 5 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

[tex]\frac{1}{2}[/tex] hour = 1800 seconds

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

So,

We can write,

Distance = speed * time

3.5 * 1800 = 6300 meters    (Equation-1)

(2) 1. 6 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

[tex]\frac{1}{2}[/tex] hour = 1800 seconds

So,

We can write,

Distance = speed * time

1.6 * 1800 = 2880 meters       (Equation-2)

Then,

We can add the equation - 1 and 2,

= 6300 meters + 2880 meters  

= 9180 meters

Therefore,

Aiden run and walk in 60 ​minute, then the distance = 9180 meters

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The length of BD is approximately 22.67cm.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental result in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). It is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that it is knowledge that was already known to the ancient Babylonians and Indians.

The theorem can be written mathematically as:

c^2 = a^2 + b^2

This is a classic problem in trigonometry known as the Pythagorean theorem in a right triangle. Since BD is perpendicular to AC, we can use the Pythagorean theorem to find the length of BD, which states that in a right triangle, the square of the length of the hypotenuse (BD in this case) is equal to the sum of the squares of the other two sides (AB and AD).

So, BD^2 = AB^2 + AD^2

We are given that AB = 17cm and AD = 15cm, so we can substitute those values into the equation and solve for BD:

BD^2 = (17cm)^2 + (15cm)^2 = 289 + 225 = 514

To find the length of BD, we take the square root of both sides:

BD = √514cm

BD ≈ 22.67cm

Hence, the length of BD is approximately 22.67cm.

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The LCM of the numbers 1 - x² and (x - 1)³ is (1 - x²)(x - 1)

An equation is a expression that shows the relationship between numbers and variables.

The least common multiple (LCM) of a set of numbers is the smallest number that can be divisible by the set of numbers

Given the numbers:

1 - x² and (x - 1)³

(1 - x²) = (1 - x)(1 + x) = -1(x - 1)(x + 1)

(x - 1)³ = (x - 1)(x - 1)(x - 1)

The LCM = -1(x + 1)(x - 1)(x - 1) = -1(x² - 1)(x - 1) = (1 - x²)(x - 1)

The LCM is (1 - x²)(x - 1)

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Answer: x=-28

Step-by-step explanation:

Answer: -28

Step-by-step explanation:

1.5x+3=-39

      -3    -3

1.5x=-42

__     __

1.5     1.5

x = -28

lines mean divide

The fundamental color-programming unit on a computer screen or in a digital image is the pixel, a word that was created from the phrase "picture element." Consider it more as a conceptual than a physical unit. In a digital display, pixels are the smallest unit.

The smallest component of a visual display or digital image is a pixel, also known as a picture element. A grid of pixels is used to create computer screens. Red, blue, and green illumination components make up each pixel, which may produce millions of distinct colors by combining them in various ways and at various intensities.

For instance, a computer with a display resolution of 1280 x 768 will create up to 98,3040 pixels on a display screen. The number of pixels per inch of the monitor screen affects image quality; more pixels per inch produce better images.

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The best estimate for the perimeter of the triangle will be 23.7 inches.

In Δ ABC ∠B =90° , ∠C = 30° , ∠A = 60° and hypotenuse AC = 10 inches

It has been described in the attachment.

Now, we shall calculate side AB and BC by using Trigonometric Ratios.

Sin 30° = AB / AC

or,  AB = 10 × Sin 30° = 10 × 0.5 = 5 inches

And, Cos 30° = CB / AC

or,CB =  10 × Cos 30° = 10 × 0.866 = 8.66 inches

Now, we calculate the perimeter of the given triangle

The perimeter of the triangle is = AB + BC + CA

                                                     = (5.0 + 8.66 + 10.0 ) inches

                                                     = 23.66 inches ≈ 23.7 inches

Hence, the best estimate for the perimeter of the triangle will be 23.7 inches.

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The complete question is:

A triangle has angles that measure 30°, 60°, and 90°. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth.

The angle measure BAC is the sum of angles BAD and CAD.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Given a triangle ABC.

A line is drawn inside the triangle from vertex A to the opposite side BC.

Given that AD = BD = CD.

That is the line AD bisects the line BC.

So here we have two smaller triangles ABD and ACD.

Two corresponding sides of both the triangles are equal.

Then the third side is also equal.

AB = AC

And we get angle A is bisected.

By the angle bisector theorem,

Measure of angle BAC = Measure of angle BAD + Measure of angle CAD

Hence, Measure of angle BAC = Measure of angle BAD + Measure of angle CAD

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So on solving the provided question, we can say that fraction we have are  [tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]   = 14/6

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here the fraction we have are

[tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]

12/3 + 12/4 + 15/2

14/6

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Answer:

1. yes

2. no

3. no

4. yes

Step-by-step explanation:

Answer:

u ≤ 15

Step-by-step explanation:

=> u/3 ≤ 5

Multiplying both sides by 3

=> 3×u/3 ≤ 5 ×3

=> u ≤ 15

Answer:

A, B,D

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.

Given its three sides and three vertices, a triangles is a polygon. A fundamental geometric shape, it. Triangle ABC refers to a triangle that has the points A, B, and C as its corners. When four parts are not collinear, a solitary plane and triangle are discovered in geometric shapes. Triangles are known as polygons because of their upper right and three corners. A triangle's three points of intersection are referred to as its corners. By multiplying triple triangle angles, 180 degrees can be obtained.

Here,

The given number indicates that FG is 8 & GH is 14.

FG + GH = FH thanks to the segment addition postulate.

In the equation FG Plus GH = FH, 8 should be used in place of FG and 14 should be used in place of GH.

This results in FH = 8 + 14 => FH = 22.

Therefore, is 22 miles away.

Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.

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The complete question is " Find FH in the given triangle FGH where FG=8,GH=14 and the FH is the equal to sum of FG and GH"

The number of y-intercepts for g(x) is larger than that for f. (x). The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).

When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.

given

The graph of f(x) is moved two units to the right and three units downward to get the graph of g. (x).

The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).

Given that a>0, f(x) and g(x) are ascending parabola.

Since the origin is f(x vertex, )'s f(x) has just one y-intercept, or (0,0).

Given that g(x) is an upward parabola with a vertex at (2,-3), g(x) has two y-intercepts.

Because of this, the number of y-intercepts for g(x) is larger than that for f. (x).

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The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.

Simply put, probability measures how likely something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is mainly the study of events subject to probability.

In Population D:

Population Proportion :Turtles have shell length greater than 2 feet = 0.3

Random Sample = 40

Turtles have shell length greater than 2 feet in random sample = 15

In Population E:

Population Proportion :Turtles have shell length greater than 2 feet = 0.2

Random Sample = 60

Turtles have shell length greater than 2 feet in random sample = 11

Let  [tex]\hat{p}_D[/tex] represents sample proportion for D

Let  [tex]\hat{p}_E[/tex] represents sample proportion for E

[tex]$ \text{SampleProportion} =\frac{\text { Count of Success }}{\text { Size of the population }}$[/tex]

[tex]$$\begin{aligned}\hat{p}_D & =\frac{\text { Turtles have a shell length greater than } 2 \text { feet in random sample }}{\text { Random Sample }} \\& =\frac{15}{40} \\& =0.375\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\hat{p}_E & =\frac{\text { Turtles have a shell length greater than 2 feet in random sample }}{\text { Random Sample }} \\& =\frac{11}{60} \\& =0.183\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\text { Difference in sample proportion } & =\hat{p}_D-\hat{p}_E \\& =0.375-0.183 \\& =0.1917\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\hat{\boldsymbol{p}} & =\frac{X_1+X_2}{N_1+N_2} \\& =\frac{15+11}{40+60} \\& =0.26\end{aligned}$$[/tex]

[tex]$$\begin{aligned}Z & =\frac{\left(\hat{p}_D-\hat{p}_E\right)-\left(p_D-p_E\right)}{\sqrt{\hat{p}(1-\hat{p}) \times\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}} \\& =\frac{(0.375-0.183)-(0.3-0.2)}{\sqrt{0.26 \times 0.74 \times\left(\frac{1}{40}+\frac{1}{40}\right)}} \\& =\frac{0.0917}{\sqrt{0.1924 \times 0.04166}} \\& =0.0087\end{aligned}$$$$[/tex]

[tex]\begin{aligned}P\left(\hat{p}_D-\hat{p}_E\right. & > 0.1917) \\& =P(Z > 0.0087) \\& =1-P(Z \leq 0.0087) \\& =0.4681\end{aligned}$$[/tex]

Therefore, The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.

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Answer:

16

Step-by-step explanation:

option c 16 is the answer

The time taken by 3 electricians to complete the work is 9 1/3 hours.

When one quantity's value rises relative to another's decrease or vice versa, it is said that the two are inversely proportionate.

It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.

If x and y are inversely proportionate to each other

=> x ∝ 1/y  

=> xy = k    [ where 'k' is proportionality constant ]

Here we have

The time required to complete a job varies inversely to the number of people working. It took 4 hours for 7 electricians to wire a building.

Let x be the time and y be the number of people

Given that the time required to complete a job varies inversely to the number of people working.  

=> xy = k ---- (1)  [ Since they are inversely proportional to each other ]    

Given that it took 4 hours for 7 electricians to wire a building.  

=> 4(7) = k  

=> k = 28

Substitute k = 28 given number of electricians y = 3 in equation (1)

=> x (3) = 28

=> x = 28/3 = 9 1/3hrs

Therefore,

The time taken by 3 electricians to complete the work is 9 1/3 hours.

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Answer:

x=-9ln(1/2)/[ln(4)-ln(1/2)]

Step-by-step explanation:

4^{x}=(1/2)^{x-9}

ln(4^{x})=ln((1/2)^{x-9})

xln(4)=(x-9)ln(1/2)

xln(4)=xln(1/2)-9ln(1/2)

xln(4)-xln(1/2)=-9ln(1/2)

x[ln(4)-ln(1/2)]=-9ln(1/2)

x=-9ln(1/2)/[ln(4)-ln(1/2)]

The graph of Linear equation with colors lines black, orange, green and blue is shown in figure.

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Given that;

Linear equation with colors lines black orange green and blue.

Now, We know that;

The graph of linear equation is always a straight line.

Hence, The graph of Linear equation with colors lines black orange green and blue is shown in figure with straight line.

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The coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].

When the numerator and denominator have no common factors other than one, the fraction is in its simplest form. Use division to find the simplest form of a fraction.

Given set of points

A(-2, 5)

B(2, 3)

ratio 3:5  or  r = 3/5

We will use the following formula to find the coordinate

[tex]$x=\frac{x_1+r x _2}{1+r}[/tex]

[tex]$y=\frac{y _1+r y _2}{1+r}$[/tex]

Substitute the values in the formula

[tex]$ x=\frac{-2+(3 / 5) 2}{1+3 / 5}[/tex]                 [tex]$y=\frac{5+(3 / 5) 3}{1+(3 / 5)}[/tex]

[tex]$x=\frac{-2+6 / 5}{5+3 / 5}[/tex]                     [tex]$ y=\frac{59 / 5}{5+8 / 5}$[/tex]

[tex]$x=\frac{-10+6 / 5}{8 / 5}[/tex]                   [tex]$ y=\frac{25+9 / 5}{8 / 5}$[/tex]

[tex]$x=\frac{-4}{8}[/tex]                               [tex]$y=\frac{17}{4}$[/tex]

x = -1/2                               y = 3[tex]\frac{1}{4}[/tex]

Thus, the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].

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Full question:

Given the points A(-2, 5) and B(2, 3), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3: 5. Write the answer in lowest simplified fraction if necessary.

The exponential model indicates that plastic production has increased by 4.9% per year.

Fit an exponential model to this data

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Answer: First=Undefined (if you had a typo, please respond and I will edit)

Second=3.5

Step-by-step explanation:

-|b=2a|

-|-8=2(2.5)|

-8=5

Undefined

3|b+6|-|a|

3|-8+6|-|2.5|

3|-2|-2.5

3*2-2.5

6-2.5

3.5

The measurement 63.42 feet after conversion  is  760.92 inches.

What is conversion of measurement?

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, the right conversion factor to an equivalent value must be applied. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.

Here the given measurement is ,

=> 63.41 feet

To convert feet into inches we need to multiply by 12. Then

=> 63.41 × 12 = 760.92 inches.

Hence the given measurement into inches 760.92 inches.

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Step-by-step explanation:

multiply both equations with factors so that the terms of the targeted variable (in our case x) have the same constant factor. and then we can subtract one equation from the other, abd the variable is eliminated in the result.

in our case the least common multiple of 4 and 9 is 36.

so, we multiply equation 1 by 9, and equation 2 by 4, abd then we subtract

36x - 54y = 90

- 36x + 8y = 28

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

0 -62y = 62

so, x is "eliminated", and we can solve for y : y = -1.

and then we can use one of the original equations to solve for x.

e.g.

9x + 2×-1 = 7

9x - 2 = 7

9x = 9

x = 1

Answer:

First, we'll need to find the LCM (least common multiple) which, in this case, is 36. Now that we know this, we can get 4x and 9x to be 36x and -36x so that they can cancel out. To do this, we have to multiply Equation 1 by 9 and Equation 2 by -4.

9(4x - 6y = 10) is equivilant to 36x - 54y = 90

-4(9x + 2y = 7) is equivilant to -36x - 8y = -28

Now that we have our new system of equations, we can proceed with the process of elimination! The first step is to add the two equations together. This will result in:

-62y = 62 we have successfully eliminated x!

The last step will be to divide both sides by -62

-62y/-62 = 62/-62

y = -1