a fish tank 60 litres of water round to 1 significant figure
40 litres of water rounded to 1 significant figure is removed from the tank
work out the upper bound of the water left in the tank

To solve the equation (x - 3)^2 = 49, we can take the square root of both sides to eliminate the exponent of 2. However, when taking the square root, we need to consider both the positive and negative square roots.

(x - 3)^2 = 49

Taking the square root of both sides, we get:

√((x - 3)^2) = ±√49

Simplifying, we get:

x - 3 = ±7

Adding 3 to both sides, we get:

x = 3 ± 7

So the possible values of x are:

x = 3 + 7 = 10

x = 3 - 7 = -4

Therefore, the correct values of x are -4 and 10. The options given are -46, -4, 10, and 52. So the correct values of x from the options are -4 and 10.

Answer:

-4 and 10.

Step-by-step explanation:

Answer:

First graph:

y + 7 = C((x + 5)^3)

-3.8 + 7 = C(4^3)

3.2 = 64C, so C = .05

y = .05((x + 5)^3) - 7

Second graph:

y - 38.45 = C((x + 5)^3)

2 - 38.45 = C(4.5^3)

-36.45 = 91.125C

C = -.4

y = -.4((x + 5)^3) + 38.45

The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.

We have,

The probability of getting a head or a tail when flipping a fair coin.

= 1/2 or 0.5

Assuming the coin is unbiased and each flip is independent of the previous flips.

To find the probability of getting 9 heads out of 15 tries, we need to use the binomial probability formula:

= P(9 heads out of 15 tries)

= [tex]^{15}C_9[/tex] x (0.5)^9 x (0.5)^6

Now,

P(9 heads out of 15 tries)

= 5005 x (0.5)^9 x (0.5)^6

= 0.19638 (rounded to five decimal places)

Thus,

The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.

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Answer:

8 centimeters squared.

Step-by-step explanation

This is just me assuming flower was flat???

The triangle was regular, so it measured 4 by 4 by 4. Triangle formula is 1/2bh.

1/2bh

1/2*4*4

2*4

8

There are 30 minutes in [tex]\frac{2}{4}[/tex] of an hour.

To find the no. of minutes in an hour we can multiply the no. of hours by 60. Suppose to find the no. of minutes in an hour we can simply multiply 1 by 60 so we can get 60 minutes in an hour.

Similarly to find the no. of minutes are in [tex]\frac{2}{4}[/tex] of an hour we can multiply the [tex]\frac{2}{4}[/tex] by 60 to get the required minutes.

[tex]\frac{2}{4}[/tex] × 60 = [tex]\frac{1}{2}[/tex] × 60 = [tex]\frac{60}{2}[/tex]  = 30.

So, from the above explanation, we can conclude that there will be 30 minutes in the [tex]\frac{2}{4}[/tex] of an hour.

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The line of reflection is the line y = 0, which is the x-axis.

To see this, imagine folding the image of polygon VWYZ along the x-axis so that the top vertex, V, is reflected down to its corresponding point, V'. Similarly, W is reflected up to W', Y is reflected up to Y', and Z is reflected down to Z'. This produces the image of polygon V'W'Y'Z', which is the reflection of polygon VWYZ across the x-axis.

When reflecting a shape across a line, the line of reflection is the line that serves as the "mirror" for the shape. In this case, the given polygons VWYZ and V'W'Y'Z' are related by a reflection. By examining the vertices of the polygons, we can determine the line of reflection. The x-coordinates of the corresponding vertices are the same, which suggests that the line of reflection is vertical.

However, the y-coordinates are opposites, indicating that the line of reflection is actually the x-axis. Therefore, the reflection of polygon VWYZ onto polygon V'W'Y'Z' is achieved by folding the image along the x-axis so that each vertex is reflected across the x-axis to its corresponding point in the other polygon.

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Answer:

Reflection across x = −1

Step-by-step explanation:

Took test it's right!

well the first cylinder is small the other is big and if this dosent help i'm so very sorry

Answer:

327

Step-by-step explanation:

To calculate how much Francisca and Elizabeth will raise together, we need to know how many laps or miles they walked. Unfortunately, the problem doesn't provide us with that information.

However, we can calculate how much each girl will raise individually.

Francisca will walk for 3 hours which is equal to 6 half-hours. She raises $25.50 every half-hour so she will raise:

$25.50 x 6 = $153

Elizabeth will walk for 3 hours which is equal to 12 quarter-hours. She raises $14.50 every quarter-hour so she will raise:

$14.50 x 12 = $174

Therefore, Francisca and Elizabeth will raise a total of:

$153 + $174 = $327

The area of the circle is 50.24.

The area of the square is 32.

The area of the shaded region is 18.24.

We have,

From the figure,

Area of the circle.

= πr²

Radius = 4

So,

= 3.14 x 4 x 4

= 50.24

In the triangle QST,

TS and TQ are congruent.

TS = TQ = x

QS = 8

This means,

From the Pythagorean theorem,

8² = x² + x²

64 = 2x²

x² = 32

x = √(16 x 2)

x = 4√2

Area of the square.

= Side²

Side = x = 4√2

= (4√2)²

= 16 x 2

= 32

Now,

Area of the shaded region.

= Area of the circle - Area of the square

= 50.24 - 32

= 18.24

Thus,

The area of the circle is 50.24.

The area of the square is 32.

The area of the shaded region is 18.24.

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The toast will land with buttered side 50% of the time.

First,

H₀:p=0.5, H₁: p₀ ≠0.5

P(butttered side down)= 19/51

π₀= 0.5

n= 51

Now, z = (p- π₀)/ √π₀(1-π₀)/n

z= (19/51 -0.5)/√0.5(1-0.5)/51

z= -1.82

as, α= 0.01 and [tex]z_{\alpha/2[/tex]=  2.58

So, |z| < | [tex]z_{\alpha/2[/tex]|

Thus, it reject H₀.

Thus, the toast will land with buttered side 50% of the time.

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Step-by-step explanation:

If slope r and slope m are perpendicular , their product must give negative one.

That is r ×m = -1

r = -1 /m

m = -1 /r

The value of x is 50° from the given set of parallel lines.

Give that, two parallel lines cut by a transversal.

The interior angles are (2x+10)° and (2x-30)°.

Here, (2x+10)°+(2x-30)°=180° (Sum of co-interior angles is 180°)

4x-20=180

4x=200

x=200/4

x=50°

Therefore, the value of x is 50° from the given set of parallel lines.

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The angle of elevation is 53.1( nearest tenth)

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. Trigonometric ratio is mainly used to solve problems in this case.

A 20ft ladder leans against the wall, the height of the wall will be the opposite to angle of elevation and the height of the ladder will be the hypotenuse.

Therefore using trigonometry ratio;

sin( tetha) = opp/hyp

sin(tetha) = 16/20

sin(tetha) = 0.8

tetha = sin^-1(0.8)

tetha = 53.1°( nearest tenth)

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Answer:

True

Step-by-step explanation:

Peach snack packs averagely cost more than apple snack packs so a reasonable solution can be P is greater than A

Answer:

a)

[tex]4ydy = xdx[/tex]

[tex]2 {y}^{2} = \frac{1}{2} {x}^{2} + c[/tex]

[tex] {y}^{2} = \frac{1}{4} {x}^{2} + c [/tex]

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

b)

c = 4, so

[tex] {y}^{2} = \frac{1}{4} {x}^{2} + 4[/tex]

[tex]y = - \sqrt{ \frac{1}{4} {x}^{2} + 4} [/tex]

[tex]y = - \frac{ \sqrt{ {x}^{2} + 16} }{2} [/tex]

When x = 1/2 and y = 4, the value of the expression (4x + 6)/8y is 1/4.

We have,

The expression is (4x + 6)/8y.

Substituting x = 1/2 and y = 4 in the given expression.

= (4x + 6)/8y

= (4(1/2) + 6)/8(4)

= (2 + 6)/32

= 8/32

= 1/4

Therefore,

When x = 1/2 and y = 4, the value of the expression (4x + 6)/8y is 1/4.

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The values of the given problems are:

Using angle sum and difference identities, we can calculate:

sin(75°) = sin(45°)cos(30°) + cos(45°)sin(30°)

sin(15°) = sin(45°)cos(30°) - cos(45°)sin(30°)

Then, we find:

sin(75°) + sin(15°) =

[sin(45°)cos(30°) + cos(45°)sin(30°)] + [sin(45°)cos(30°) - cos(45°)sin(30°)]

≈ 1.22

sin(75°) - sin(15°) =

[sin(45°)cos(30°) + cos(45°)sin(30°)] - [sin(45°)cos(30°) - cos(45°)sin(30°)]

≈ 0.71

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The Complete Question

Select the correct answer from each drop-down menu.

sin75° +sin15°=

sin75°-3in15º =

Answer:

it's 0

Step-by-step explanation:

I don't know it's answer you have to ask it to the teacher

The event lasted for 11,700 seconds.

Time is an essential concept that we use to measure the duration of events. In this context, let's consider an event that lasts for 3 hours and 15 minutes.

To convert time from hours and minutes to seconds, we need to know the number of seconds in an hour and a minute.

There are 60 minutes in an hour, and each minute has 60 seconds.

=> (3 x 60 x 60) = 10,800

=> 15 x 60 = 900

To find the total time of the event, we need to add the time in seconds for the hours and minutes, which is

=> 10,800 seconds + 900 seconds = 11,700 seconds.

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Answer:

To determine the range of car prices for which the cash-back option will cost less, we need to find the total cost of each option over 60 months for different car prices and compare them. Let's assume the car price ranges from $20,000 to $30,000.

For the 0% financing option, the monthly payment is $16.67 per $1,000 financed, so the monthly payment for a car priced at $20,000 would be:

$20,000 / 1000 * $16.67 = $333.40 per month

Similarly, the monthly payment for a car priced at $30,000 would be:

$30,000 / 1000 * $16.67 = $500.10 per month

Over 60 months, the total cost for the 0% financing option for a car priced at $20,000 would be:

$333.40 * 60 = $20,004

And the total cost for a car priced at $30,000 would be:

$500.10 * 60 = $30,006

For the cash-back option, the cost of the car would be reduced by $2,500, so the total cost over 60 months for a car priced at $20,000 would be:

($20,000 - $2,500) + ($18.41 * $20) * 60 = $19,484

And the total cost for a car priced at $30,000 would be:

($30,000 - $2,500) + ($18.41 * $30) * 60 = $29,222

To find the range of car prices for which the cash back option will cost less, we need to compare the total cost of each option. Setting the two equations equal to each other and solving for x, we get:

($x - $2,500) + ($18.41 * $x) * 60 < $20,004

($x - $2,500) + ($18.41 * $x) * 60 > $30,006

Simplifying, we get:

$17.285x < $22,504

$17.285x > $34,256

Dividing by 17.285, we get:

$1,300.90 < x < $1,978.63

So, for car prices between $13,000.90 and $19,978.63, the cash-back option will cost less.

To find the range of car prices for which the 0% financing option is a better choice, we can simply look at the range of car prices for which the cash-back option is more expensive, which is anything outside of the range of $13,000.90 to $19,978.63. Therefore, for car prices outside of this range, the 0% financing option is the better choice.

As the sample size increases, it does not necessarily mean that the range of the sample population also increases.

The range of a sample population is simply the difference between the maximum and minimum values of the data set. It is possible for the range to increase or decrease as the sample size increases, depending on the distribution of the data.

For example, if the data is evenly distributed with no outliers, increasing the sample size may not change the range significantly. However, if the data has outliers or a skewed distribution, increasing the sample size may result in capturing more extreme values, which could increase the range of the sample population.

Therefore, it is important to consider the distribution of the data and not assume that increasing the sample size will always result in an increased range of the sample population.

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1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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Answer: 5/21

Step-by-step explanation: it just is

the answer is 5/21 (0.23)

Answer:

x = 21.1

y = 18.3

Step-by-step explanation:

                      left triangle     right triangle     large triangle

Short leg:             12                  altitude                    y

Long legs:        altitude                 16                         x

Hypotenuse:         y                       x                          28

The three triangles are similar, so the ratios of the lengths of corresponding sides are equal.

hypotenuse/short leg

28/y = y/12

y² = 12 × 28

y² = 336

y = 18.3

hypotenuse/long leg

28/x = x/16

x² = 28 × 16

x² = 448

x = 21.1

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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The sum of interior angles in the polygon is 3240 degrees.

The equation used to find x is 180 = 12x - 6.

We have,

The sum of the interior angles of a polygon with n sides can be calculated using the formula (n-2) x 180 degrees.

So, for a regular icosagon with 20 sides, the sum of interior angles.

= (20-2) x 180

= 3240 degrees.

Therefore, the answer is option C, 3240.

Part B:

The sum of the interior angles of a regular polygon can also be calculated using the formula:

Sum of interior angles = n(180 - exterior angle)/2,

where n is the number of sides.

For a regular icosagon, the exterior angle can be found by subtracting the interior angle from 180 degrees.

= 180 - (12x - 6)

= 186 - 12x.

Substituting the values in the formula, we get:

3240 = 20(180 - (12x - 6))/2

Simplifying this equation, we get:

3240 = 1800 - 60x + 30

Combining like terms, we get:

1410 = -60x

Dividing both sides by -60, we get:

x = -23.5

Therefore,

The sum of interior angles is 3240 degrees.

The equation used to find x is 180 = 12x - 6.

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Answer: the last option is correct

Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:

r = √((-7√3/2)^2 + (7/2)^2)

θ = atan2(7/2, -7√3/2)

Simplifying the expressions:

r = √(147/4 + 49/4) = √(196/4) = √49 = 7

θ = atan2(7/2, -7√3/2)

Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:

θ ≈ 5π/6

So the correct answer is: (7, 5π/6), which is option (6).

An important concept of unit circle in geometry and trigonometry is it helps us to understand and visualize the values of sine, cosine, and tangent functions for different angles.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane.

The coordinates of points on the unit circle correspond to the values of sine and cosine of the corresponding angle.

For example, if we draw a line from the origin to a point on the unit circle that makes an angle of θ with the positive x-axis.

The x-coordinate of that point is cos(θ) and the y-coordinate is sin(θ).

The unit circle is also useful for understanding and visualizing the properties of periodic functions, such as sine and cosine.

Since sine and cosine are periodic with a period of 2π, the unit circle repeats itself every 2π radians or 360 degrees.

Which makes it easier to analyze and graph these functions.

In addition, the unit circle helps us understand the relationships between trigonometric functions.

Pythagorean identity (sin²(θ) + cos²(θ) = 1) is a fundamental relationship that is easy to see and prove using the unit circle.

Overall, the unit circle is an important concept that provides a visual and geometric representation of trigonometric functions and their properties.

It can be a useful tool for solving problems in geometry and trigonometry.

As well as for understanding more advanced concepts in calculus and other branches of mathematics.

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