OPTIONAL - Space to calculate your work.
REQUIRED
1
9.
How much water can Portia’s new aquarium hold?

a) 166.28 cubic inches

b) 790.28 cubic inches

c) 956.56 cubic inches

d) 3,120 cubic inches

e) 6,240 cubic inches
REQUIRED
1
10.
Portia's new fish require complete darkness for 12 hours a day. Rather than buying a blackout curtain for her room, she decides to make an aquarium cover out of a tropical print, with a blackout liner. How much tropical print fabric will she need to purchase in order to cover the top and sides of the aquarium?

a) 864 square inches

b) 624 square inches

c) 1,144 square inches

d) 1,104 square inches

e) 480 square inches

Answer:

when you use the numbers that are given you can see that B is the right answer

Answer:

12

Step-by-step explanation:

The given sequence is an arithmetic sequence where the difference between one number and the previous number is -6

For example, 30 - 36 = -6

24-30 = -6

18 - 24 = -6

This constant difference is known as the common difference

The next number in the sequence will be 6 less than 18 = 18-6 = 12

Step-by-step explanation:

Use the interest formula   P rt    then add it to P

   P = principal (900)  r = decimal interest per period ( 5% = .05)  t = 4 years

  P rt  + P = 900 ( .05)(4)  + 900 = $ 1080

The distance it will take to drive from Toronto to buffalo (distance between Toronto and buffalo is 154km) is 1.75 hours.

We are given that;

distance = 154 km speed = 88 km/hr

Now,

we need to use the formula:

time = distance / speed

where time is in hours, distance is in kilometers, and speed is in kilometers per hour.

Plugging these values into the formula, we get:

time = 154 / 88 time ≈ 1.75

Therefore, by speed the answer will be 1.75 hours.

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[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =\frac{7\pi }{6} \end{cases}\implies s=5\left( \cfrac{7\pi }{6} \right)\implies s=\cfrac{35\pi }{6}\implies s\approx 18.33[/tex]

Answer:

5 cm

Step-by-step explanation:

because the equal chords are equdistant

The length of ZY, given that in ΔXYZ, ∠Y = 90°, ∠X = 34°, ∠ZWY = 60° and XW = 7.2 is 8.2

The following data were obtained from the question:

From the attached photo, we shall obtain WY. This is show below:

Tan θ = opposite / adjacent

Tan 60 = a / b

Cross multiply

b × Tan 60 = a

Divide both sides by Tan 60

b = a / Tan 60

b = 0.6a

Finally, we shall determine the length of ZY. Details below:

Tan θ = opposite / adjacent

Tan 34 = a / 7.2 + 0.6a

Cross multiply

Tan 34 (7.2 + 0.6a) = a

4.9 + 0.4a = a

Collect like terms

4.9 = a - 0.4a

4.9 = 0.6a

Divide both sides by 0.6

a = 4.9 / 0.6

a = 8.2

Thus, we can conclude that the length of ZY is 8.2

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The required related probability statement is P(-1.65 < z < 1.65) = 0.901 or 90.1%.

Find the area under the standard normal curve that lies between z = -1.65 and z = 1.65.

Remember, these steps can be applied to other problems involving the standard normal curve to find probabilities or areas associated with specific ranges of values.'

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The areas of the composite figures are listed below:

Case 13: A = 198 mm²

Case 14: A = 52.069 mm²

In this problem we find two composite figures, whose areas are determined with the help of the following area formulas:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Semicircle

A = 0.5π · r²

Where:

Now the area for each case is introduced below:

Case 13

A = 0.5 · (12 mm) · (15 mm) + (12 mm) · (9 mm)

A = 198 mm²

Case 14

A = 0.5π · (4.5 mm)² + (4.5 mm)²

A = 52.069 mm²

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Answer:

By elimination method:

e.

4x - y = 0

12x - 6y = 24

We can use the method of substitution. From the first equation, we have y = 4x. We substitute this value of y into the second equation:

12x - 6(4x) = 24

12x - 24x = 24

-12x = 24

x = -2

Substituting the value of x back into the first equation:

4(-2) - y = 0

-8 - y = 0

y = -8

Therefore, the solution to the system of equations is x = -2 and y = -8.

f.

3x + 15y = 3

2x - 5y = -28

We can use the method of elimination. Multiply the first equation by 2 and the second equation by 3 to eliminate x:

6x + 30y = 6

6x - 15y = -84

Subtract the second equation from the first equation:

(6x + 30y) - (6x - 15y) = 6 - (-84)

45y = 90

y = 2

Substitute the value of y into one of the original equations:

3x + 15(2) = 3

3x + 30 = 3

3x = -27

x = -9

Therefore, the solution to the system of equations is x = -9 and y = 2.

g.

3x + 2y = 10

6x + 4y = 15

We can again use the method of elimination. Multiply the first equation by 2 to eliminate y:

6x + 4y = 20

6x + 4y = 15

Since the equations are the same, we have infinitely many solutions. This means that any values of x and y that satisfy the equation 3x + 2y = 10 will be a solution to the system. They are parallel.

h.

4x - 6y = -26

-2x + 3y = 13

Again, we can use the method of elimination. Multiply the second equation by 2 to eliminate x:

4x - 6y = -26

-4x + 6y = 26

Add the two equations:

0 = 0

Since the equations are equivalent, we also have infinitely many solutions. Any values of x and y that satisfy the equation 4x - 6y = -26 will be a solution to the system. They are the same straight line.

Answer:

A = 378 in²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here b₁ = 6 + 15 + 6 = 27 , b₂ = 15 ( equal to middle section of b₁ ), h = 18, so

A = [tex]\frac{1}{2}[/tex] × 18 × (27 + 15) = 9 × 42 = 378 in²

Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

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if d = 14 cm ----> r = d/2

hence, circumference of a circle is:

[tex]c = 2\pi \: r \\ c = 2 \times \pi \times \frac{14}{2} = 14\pi \: cm[/tex]

and its unit is centimeters or cm

The curved surface area of the cylinder is 48.06 cm².

The circumference of a cylinder is given by the formula:

C = 2πr

where C is the circumference and r is the radius of the base.

In this case, the given circumference is 6 cm.

So, 6 = 2πr

r = 6 / (2π)

r ≈ 0.955 cm

Now, the curved surface area (CSA) of the cylinder using the formula:

CSA = 2πrh

Given the height as 8 cm, we can substitute the values into the formula:

CSA = 2π(0.955 cm)(8 cm)

CSA ≈ 48.06 cm²

Therefore, the curved surface area of the cylinder is 48.06 cm².

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Note that the function that  is continuous across its domain is C. f(x) = {x + 4, -4 ≤ x < -2; 0.5x², -2 ≤ x < 4; 20 - 3x, 4 ≤ x ≤ 8}

To determine which function is continuous across its domain, we need to ensure that there are no abrupt jumps, breaks, or undefined points within the given intervals.

In option C, the function is defined and continuous within each interval [-4, -2), (-2, 4), and [4, 8]. It consists of three separate pieces that are individually continuous, and there are no breaks or undefined points within each interval.

In options A and B, there are abrupt changes or discontinuities at x = 4 where the function switches to a different expression. This makes the function discontinuous at x = 4.

Therefore, option C is the correct answer as it represents a function that is continuous across its domain.

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Answer:

[tex]b^\frac{5}{12}[/tex]

Answer:

231623.3 m³

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

Volume of hemisphere = (2/3) X π X r ³

= (2/3) π (48)³

= 73728π

= 231623.3 m³ to nearest tenth

The length of KO in the given segment is 8 units.

Given:

The segment KO can be broken into two equal portions at point N since N is the segment's midpoint. KN thus equals NO.

KN can be divided into two equal pieces at point L, which serves as the segment's halfway. KL = LN as a result.

LN can be divided into two equal pieces at point M, which serves as the segment's halfway. ML thus equals MN.

The following relationships can be inferred from the information provided:

KL = LN

ML = MN = 2

The length of KO must be determined. We can utilize the following relationships to accomplish this:

KL + LN = KN (by adding the two equations)

KL + KL = KN (since KL = LN)

2KL = KN

Let's now replace the known values:

2 + 2 = KN

4 = KN

Since N is the midpoint of KO, KN = NO.

Therefore, NO = 4.

By combining the lengths of KN and NO, we can finally get the length of KO:

KO = KN + NO = 4 + 4 = 8

Hence, the length of KO is 8.

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The value for the unknown side length, x in simplest radical form is [tex]\sqrt{65}[/tex].

Based on the figure that is been provided , it can be deduced that the length of the line separating the two triangles is 4 which an be found using the Pythagoras theorem as

[tex]5^{2} = 3^{2} + y^{2} \\\\y^{2} = 25 -9\\\\y^{2} =16\\y=\sqrt{16} \\y=4[/tex]

Then the line dividing the triangle is been named y and it is 4., then we calculate the value of x as;

[tex]x^{2} = 7^{2} + 4^{2} \\x^{2} = 49 + 16\\ x^{2} = 65\\x=\sqrt{65}[/tex]

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The desired expression would be k / 100,000.

Start with the value 10.

In other words, you're taking the value of k and dividing it by 100,000, which is the result of raising 10 to the power of 5.

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Answer:

x = (v - u) / a

Step-by-step explanation:

v = u + ax.

subtract u from both sides:

v - u = ax.

divide both sides by a:

(v - u) / a = x.

so x = (v - u) / a.

this can also be written v/a - u/a

By adding the cost of 2 child passes to each expression, Leah includes the cost of 2 more children going on the trip.

We have,

To include the cost of 2 more child passes in the expressions 3(a + c) and 3a + 3c,

We can simply add the cost of 2 child passes to each expression.

Let's assume the cost of each child pass is represented by the variable "p".

To modify 3(a + c), we add the cost of 2 child passes to the expression:

3(a + c) + 2p

This represents the total cost of 3 passes for children, including the original "a" and "c" passes, as well as the additional 2 passes.

To modify 3a + 3c, we also add the cost of 2 child passes:

3a + 3c + 2p

This represents the total cost of 3 passes for children, including the original "a" and "c" passes, as well as the additional 2 passes.

Thus,

By adding the cost of 2 child passes to each expression, Leah includes the cost of 2 more children going on the trip.

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Answer:

23 is A, 24 is C, 25 is C, and 27 is B

Answer:

to find the least common multiple (LCM) of 18 and 22, you can use the following steps:

Prime factorize the numbers:

18 = 2 * 3^2

22 = 2 * 11

Identify the highest power of each prime factor that appears in either number:

The highest power of 2 is 2^1.

The highest power of 3 is 3^2.

The highest power of 11 is 11^1.

Multiply these highest powers together:

2^1 * 3^2 * 11^1 = 66.

Therefore, the least common multiple (LCM) of 18 and 22 is 66.

Step-by-step explanation:

Answer: the answer i got was b

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable in the polynomial. In the polynomial [tex]\bold{\frac{1}{4} y^7-5y^2+3y+8}[/tex], the highest power of y is 7. Therefore, the degree of the polynomial is 7.

Here is a breakdown of the degrees of each term in the polynomial:

[tex]\bold{\frac{1}{4} y^7: degree \:7 }\\\bold{-5y^2: degree \:2}\\\bold{3y: degree \:1}\\\bold{8: degree\: 0}}[/tex]

The degree of a polynomial is the highest degree of any term in the polynomial. In this case, the highest degree is 7, so the degree of the polynomial is 7.

In the given diagram, the area of the figure is approximately 146.3 cm²

From the question, we are to determine the area of figure in the given diagram

The area of the figure = Area of the semicircle + Area of rectangle + Area of  the semicircle

The formula for the area of a semicircle is

Area = 1/2 πr²

Where r is the radius

The area of a rectangle is

Area = Length × Width

In the given diagram,

The diameter of the semicircle = 8 cm

Therefore,

Radius = 4 cm

Thus,

Area of the figure = 1/2 π × 4² + (12 × 8) + 1/2 π × 4²

Area of the figure = (12 × 8) + π × 4²

Area of the figure = (96) + π × 16

Area of the figure = 96 + 16π

Area of the figure = 96 + 50.2655

Area of the figure = 146.2655 cm²

Area of the figure ≈ 146.3 cm²

Hence,

The area of the figure is 146.3 cm²

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Two different types of data used in the health field are said to be:

Blood pressure is seen as a number that measures the force of blood on vessel walls. Blood pressure values are said to be quantitative, including systolic and diastolic measurements (e.g. 120/80 mmHg). They can be added, subtracted, or averaged.

Age is qualitative, representing an attribute rather than a quantity. Blood pressure and age data collection methods will depend on research objectives and resources.

Systematic sampling can gather blood pressure data by selecting every nth person from a list for equal representation.

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The measure of minor arc AC, when CB is a diameter of the circle, is 110 degrees.

In a circle where CB is a diameter, the measure of the minor arc AC is 110 degrees.

When CB is a diameter, it means that AC is a subtended arc, meaning it is formed by the two endpoints of a chord (in this case, A and C).

The measure of an arc is defined as the central angle it subtends at the center of the circle.

Therefore, the angle at the center of the circle that corresponds to the minor arc AC is also 110 degrees.

This means that if we were to draw a line from the center of the circle to point A, and another line from the center to point C, the angle between these lines would measure 110 degrees.

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