1. A cube of sugar is 2 cm wide. Calculate the num- ber of cubes in a box 720 cm².2. Calculate the amount of air in a room 6 m long, 5 m wide and 3 m high.3. The area of one side of a cuboid is 360 cm². What is the length, if the width is 1.5 cm? 4What is the volume of a container if it contains 12 boxes each 2.5 cm by 3 cm by 4.5 cm?5. A tank contains 4 500/ of water. Find the depth of the tank if its base area is 300 m².​

Vertical Angles

---Vertical angles are congruent and can often be found where two lines intersect and make an "X" shape.

The vertical angles in this figure are XAW and UAY.

Adjacent angles that are neither complementary nor supplementary

---Adjacent angles are angles that share a line and are, as a result, next to each other.

Two adjacent angles in this figure that are neither complementary nor supplementary are XAW and ZAY.

Supplementary Angles

---Supplementary angles form a straight line, or 180 degree angle.

The supplementary angles in this figure are XAW and WAU.

Complementary Angles

---Complementary angles form a right, or 90 degree angle.

The complementary angles in this figure are XAW and XAZ.

Hope this helps!

Step-by-step explanation:

See image

Answer:

Step-by-step explanation:

150 mile length. We can make an inequality for this with him riding on his bike for r and walking for w.
40r + 4w = 150

r + w = 6

Then we get

r = 7/2

w = 5/2

The difference between the interquartile range of Matt's and Linda's remaining vacation days is 1.5.

The interquartile range will be calculated through the formula -

[tex] Q_{3}[/tex] = [tex] Q_{2}[/tex] - [tex] Q_{1}[/tex]

Firstly calculating [tex] Q_{3}[/tex] for Matt

[tex] Q_{2}[/tex] = (4+5)/2

[tex] Q_{2}[/tex] = 4.5

[tex] Q_{3}[/tex] = (8+12)/2

[tex] Q_{3}[/tex] = 10

Finding interquartile range now -

[tex] Q_{3}[/tex] = 10 - 4.5

[tex] Q_{3}[/tex] = 5.5

Now, performing calculation for Linda

[tex] Q_{2}[/tex] = (0+10)/2

[tex] Q_{2}[/tex] = 5

[tex] Q_{3}[/tex] = (11+13)/2

[tex] Q_{3}[/tex] = 12

Finding interquartile range now -

[tex] Q_{3}[/tex] = 12 - 5

[tex] Q_{3}[/tex] = 7

The difference between the interquartile range of Linda and Matt will be calculated as:

Difference = Interquartile range of Linda - Interquartile range of Matt (as we see Linda has greater interquartile range than Matt)

Difference = 7 - 5.5

Difference = 1.5

Hence, the difference between interquartile range of days is 1.5.

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The piecewise linear equation is y = -0.556x - 2.444, -8 ≤ x ≤ 1, y = 1.333x - 4.333, 1 < x ≤ 4 and y = -0.667x - 3.667 4 < x ≤ 10

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

X: -8, 1, 4, 10

Y: 2, -3, 1, -3

In the interval [-8, 1], we have

X: -8, 1

Y: 2, -3

A linear equation is represented as

y = mx + c

Using the points, we have

-8m + c = 2

m + c = -3

So, we have

m = -0.556

c = -2.444

So, we have

-0.556x - 2.444, -8 ≤ x ≤ 1

In the interval (1, 4], we have

X: 1, 4

Y: -3, 1

Using the points, we have

m + c = -3

4m + c = 1

So, we have

m = 1.333

c = -4.333

So, we have

1.333x - 4.333, 1 < x ≤ 4

In the interval (4, 10], we have

X: 4  10

Y: 1   -3

Using the points, we have

4m + c = 1

10m + c = -3

So, we have

m = -0.667

c = 3.667

So, we have

-0.667x - 3.667 4 < x ≤ 10

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Friday has a 60% chance of rain. This indicates a relatively high Probability of rainfall, making it more likely to experience wet conditions on Friday.

The weather table provides information on the chance of rain for five consecutive days, starting from Monday to Friday. Here are the details:

Day of the Week | Chance of Rain

----------------|---------------

Monday          | 70%

Tuesday         | 10%

Wednesday    | 40%

Thursday        | 50%

Friday             | 60%

According to the table, Monday has the highest chance of rain with a probability of 70%. This indicates that there is a relatively high likelihood of rain occurring on Monday. However, it does not guarantee that it will rain, as there is still a 30% chance of a dry day.

On Tuesday, the chance of rain drops significantly to 10%. This suggests that it is highly unlikely for rain to occur on Tuesday, with a higher probability of dry weather.

Wednesday shows a moderate chance of rain at 40%. This indicates a somewhat higher possibility of precipitation compared to Tuesday but not as high as Monday.

Thursday follows with a 50% chance of rain. This suggests an even chance of rain or no rain, making it relatively uncertain.

Finally, Friday has a 60% chance of rain. This indicates a relatively high probability of rainfall, making it more likely to experience wet conditions on Friday.

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Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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Answer:

[tex]\\[/tex]

Step-by-step explanation:

In the first year, the trainers will be worth 80% of their original value, which is:

[tex]\rm\implies{£100 \times 0.8 = £80}[/tex]

[tex]\\[/tex]

In the second year, they will be worth 80% of their value after the first year:

[tex]\rm\implies{£80 \times 0.8 = \boxed{\boxed{\sf{\:\:\:\green{£64}\:\:\:}}}}[/tex]

[tex]\\[/tex]

[tex]\\[/tex]

[tex]\therefore[/tex] The trainers will be worth £64 in 2 years' time.

The actual width of the soccer field is 60 yards.

Given, the scale of the drawing is 1 inch : 5 yards.

The width of the soccer field in the drawing is 12 inches.

So, the actual width of the soccer field can be found by multiplying the width in the drawing by the scale factor:

Actual width = Width in drawing x Scale factor

The scale factor is 5 yards per inch, so we can write:

Actual width = 12 inches x 5 yards per inch

Actual width = 60 yards

Therefore, the actual width of the soccer field is 60 yards.

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The solution to the given logarithmic expression is: x = 111.63

The logarithmic form of expression is written as [tex]log_{a} c = b[/tex]. This is simply a rearrangement of the specific exponential form, aᵇ = c. Thus, we can say that exponential equation could be written as a logarithm.

We want to solve the logarithmic expression given as:

log x = [tex]\frac{log 27}{log 5}[/tex]

log x = [tex]\frac{log 3^3}{log 5}[/tex]

log x = [tex]\frac{3 log 3}{log 5}[/tex]

log x = 2.0478

x = [tex]10^{2.0478}[/tex]

x = 111.63

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Prove in below steps:

Proved

The probability that both marbles are the same color is 1/3.

P(R₂ | R₁) = 1/3

The probability of both events happening together (drawing two red marbles) is the product of the probabilities of each event:

P(R₁ and R₂) = P(R₁) * P(R₂ | R₁)

= (1/2) * (1/3)

= 1/6

P(B₁) = 2/4 = 1/2

P(B₂ | B₁) = 1/3

Probability of B₁ and B₂

P(B₁ and B₂)

= P(B₁) * P(B₂ | B₁)

= (1/2) * (1/3)

= 1/6

P(Same color)

= P(R₁ and R₂) + P(B₁and B₂)

= 1/6 + 1/6 = 2/6

= 1/3

So, the probability that both marbles are the same color is 1/3.

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The solution for t is t = log(28/3) / 2,  the Logarithm in base-10.

The equation -3 * 10^(2t) = -28 for t,  the exponential term and then take the logarithm of both sides. Let's go through the steps:

Step 1: Divide both sides of the equation by -3:

(10^(2t)) = -28 / -3

Step 2: Simplify the right-hand side:

(10^(2t)) = 28/3

Step 3: Take the logarithm of both sides using base-10 logarithm (log):

log(10^(2t)) = log(28/3)

Step 4: Apply the power rule of logarithms to bring down the exponent:

2t * log(10) = log(28/3)

Step 5: Since log(10) = 1, we have:

2t = log(28/3)

Step 6: Divide both sides of the equation by 2:

t = log(28/3) / 2

Therefore, the solution for t is t = log(28/3) / 2, where log represents the logarithm in base-10.

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well, here is your pie...

The probability of drawing an orange marble and a blue marble without replacement is:P(Orange and Blue without replacement) = (3/10) * ((N - 4) / (N - 1))

The probability of drawing an orange marble and a blue marble without replacement, we need to consider the total number of marbles and the number of desired outcomes.

Let's assume we have a bag of marbles containing both orange and blue marbles. The total number of marbles in the bag is not given, so we'll consider it as an unknown value, denoted as N.

First, we need to calculate the probability of drawing an orange marble on the first draw. Since there is no replacement, the probability of drawing an orange marble on the first draw is given by the ratio of the number of orange marbles to the total number of marbles:

P(Orange on first draw) = Number of orange marbles / Total number of marbles

Next, after the first marble is drawn, the bag will contain one less marble, and the number of orange marbles and blue marbles will change accordingly. Assuming we drew an orange marble on the first draw, the number of orange marbles will decrease by 1, and the total number of marbles will decrease by 1.

Now, we need to calculate the probability of drawing a blue marble on the second draw, given that an orange marble was drawn on the first draw. The probability is calculated as:

P(Blue on second draw | Orange on first draw) = Number of blue marbles / Total number of marbles after the first draw

Since there is no replacement, the total number of marbles after the first draw is N - 1.

Finally, to find the probability of drawing an orange marble and a blue marble without replacement, we multiply the probabilities of the two events:

P(Orange and Blue without replacement) = P(Orange on first draw) * P(Blue on second draw | Orange on first draw)

To simplify the calculation, we can substitute the given values:

P(Orange on first draw) = 3/10 (assuming there are 3 orange marbles out of 10 marbles in total)

P(Blue on second draw | Orange on first draw) = (N - 4) / (N - 1) (assuming there are N - 4 blue marbles left in the bag after drawing an orange marble)

Therefore, the probability of drawing an orange marble and a blue marble without replacement is:

P(Orange and Blue without replacement) = (3/10) * ((N - 4) / (N - 1))

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The area of the sector is approximately 9.25 ft².

We have,

The formula for the area of a sector.

A = (θ/360°) × πr²

where A is the area of the sector, θ is the central angle in degrees, and r is the radius.

Substituting the given values.

A = (40°/360°) × 3.14 × (16.7 ft)²

A = 0.1111 × 3.14 × 278.89 ft²

A = 9.2465 ft²

Rounding to the nearest hundredth.

A ≈ 9.25 ft²

Therefore,

The area of the sector is approximately 9.25 ft².

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Answer:

a. Since blue occurs a fraction z of the time and the red and green portions have equal area, the probability of landing on green is (1 - z)/2.

b. The area diagram for spinning the spinner twice would have three sections: blue, green, and red. Each section would be divided into three smaller sections: BB, BG, BR, GB, GG, GR, RB, RG, and RR. The diagram would show all 9 possible outcomes of spinning the spinner twice.

c. The region on the area diagram corresponding to getting the same color on the spinner twice would be the diagonal line from the upper left to the lower right, going through the GG, BB, and RR sections.

d. The probability that both spins give the same color can be calculated as follows:

- The probability of getting blue on the first spin is z.

- The probability of getting green on the first spin is (1 - z)/2.

- The probability of getting red on the first spin is (1 - z)/2.

- If the first spin is blue, the probability of getting blue again on the second spin is z. The same applies to green and red.

- Therefore, the probability of getting the same color on both spins is z^2 + ((1 - z)/2)^2 + ((1 - z)/2)^2 = z^2 + (1 - z)^2/4.

e. If you know that you got the same color twice, the probability that the color was blue can be calculated using Bayes' theorem:

- Let A be the event that you got blue twice, and let B be the event that you got the same color twice.

- Then P(A|B) = P(B|A) * P(A) / P(B), where P(A) = z^2, P(B|A) = 1, and P(B) = z^2 + ((1 - z)/2)^2 + ((1 - z)/2)^2 = z^2 + (1 - z)^2/4.

- Therefore, P(A|B) = z^2 / (z^2 + (1 - z)^2/4).

Step-by-step explanation:

Hope this helps

Answer:

h = -10

Step-by-step explanation:

The solution to the equation is h = -10. To solve for h, we need to isolate h on one side of the equation. We do this by adding 9 to both sides, subtract 4h from both sides, and add 5 to both sides. This gives us:

Negative 3 (h + 5) + 2 + 9 = 4 (h + 6) - 9 + 9

Negative 3h + 14 = 4h + 15

Negative 3h - 4h = 15 - 14

-7h = 1

h = -1/7

h = -10

For the 4-hour infusion, 1500ml of the 20% acetylcysteine solution must be made up and combined with 500ml of glucose.

To calculate the volume of acetylcysteine that needs to be added to the glucose, we can use the following formula:

The volume of acetylcysteine (in ml) = (Total amount of acetylcysteine needed in mg / Concentration of acetylcysteine in mg/ml) x 100

We have been asked to add 3000mg of acetylcysteine to 500 ml of glucose. If the concentration of the ampoule containing acetylcysteine is 20%, this means that there are 20g of acetylcysteine in 100 ml of solution, or 200mg/ml.

Using the formula above, we can calculate the volume of acetylcysteine that needs to be added as follows:

Volume of acetylcysteine = (3000mg / 200mg/ml) x 100 = 1500ml

Therefore, 1500ml of the 20% acetylcysteine solution needs to be drawn up and added to the 500ml of glucose to make the 4-hour infusion.

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Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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We can infer that the point (8, -15) was reflected over the y-axis to (-8, -15) based on the change in the x-coordinate while the y-coordinate stays the same.

The y-axis reflected the point (8, -15) over to (-8, -15).

The x-coordinate changes its sign but the y-coordinate stays the same when a point is mirrored over the y-axis.

In this instance, the y-coordinate, -15, remains constant but the x-coordinate, 8, of the original point changes to -8 in the reflected point.

This shows that the y-axis is where the reflection took place.

Imagine a coordinate plane with the x-axis running horizontally and the y-axis running vertically in order to see this.

As a vertical mirror, the y-axis reflects points on either side of it.

When a point crosses the y-axis in reflection, it effectively flips to the other side of the axis while keeping its y-coordinate.

In this case, the point (8, -15) is initially situated in the positive x-direction on the right side of the y-axis.

After reflection, it becomes (-8, -15) and appears on the left side of the y-axis in the negative x-direction.

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Answer:

The point is reflected to the Y-axis. It can be either A or B, but I mostly positive it's A.

Step-by-step explanation:

Good luck on the final module exam! I'm counting on you.

Answer:

I would go with 900 but I’m not for sure

Step-by-step explanation:

The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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Answer:

To determine which bank is more cost-effective, we need to consider how many transactions we will make per month. Let's call the number of transactions "t".

Bank A charges a flat fee of $45 per month, regardless of how many transactions we make. So the total cost of using Bank A for one month is:

Total cost for Bank A = $45

Bank B charges a monthly fee of $20, plus $0.70 for each transaction. So the total cost of using Bank B for one month is:

Total cost for Bank B = $20 + ($0.70 x t)

To determine which bank is more cost-effective, we need to find the value of "t" that makes the total cost of Bank B equal to the total cost of Bank A.

$45 = $20 + ($0.70 x t)

$25 = $0.70 x t

t = $25 / $0.70

t ≈ 36

So if we make 36 or more transactions per month, Bank A is more cost-effective. If we make fewer than 36 transactions per month, Bank B is more cost-effective.

The actual distance from the starting point to the ending point is 39.96 miles.

For someone working with the map or scaled drawing, we can define the scale factor as the ratio between a distance on the drawing or map and the corresponding actual distance in the real world.

From the question,

1.5 inches on the map = 5 miles in actual distance

1 inch on the map =  x miles

Perform cross multiplication

1 inch on the map =  (5 x 1) / 1.5  = 3.33 miles/inch (scale factor)

The scale factor can then be expressed as ratio:

5/1.5 = 1:0.3

0r

5/1.5 = 10:3

So, the actual distance between the starting point and the ending point can be found by multiplying the length on the map by the scale factor:

Actual distance = Map distance x Scale factor

Actual distance = 12 inches x 3.33 miles/inch = 39.96 miles

Therefore, the actual distance from the starting point to the ending point is approximately 39.96 miles.

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The line of symmetry for the above figure is attached accordingly.

In mathematics, symmetry with regard to a reflection is known as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry.

That is, a figure with reflectional symmetry does not alter when it is reflected. A line/axis of symmetry exists in 2D, while a plane of symmetry exists in 3D.

After inserting the symmetry lines, the above resulted in a kite.

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Answer: 5

Step-by-step explanation:45

The magnitude of the complex number -10 + 24i is 26.

We have,

Complex numbers can be represented as a combination of a real number and an imaginary number, in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Now,

To find the magnitude of a complex number, we take the square root of the sum of the squares of its real and imaginary parts.

For -10 + 24i, the real part is -10 and the imaginary part is 24.

So the magnitude:

| -10 + 24i | = √((-10)^2 + (24)^2) = √(100 + 576) = √676 = 26

Therefore,

The magnitude of -10 + 24i is 26.

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The mean of the test is 45.

Let's use the formula for z-score:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the raw score, μ is the mean, and σ is the standard deviation.

For the first score of 30, we know that it falls three standard deviations below the mean:

-3 = (30 - μ) / σ

Simplifying this equation, we get:

-3σ = 30 - μ

μ = 30 + 3σ

For the second score of 60, we know that it falls three standard deviations above the mean:

3 = (60 - μ) / σ

Simplifying this equation, we get:

3σ = 60 - μ

μ = 60 - 3σ

Now we can set these two equations equal to each other, since they both equal μ:

30 + 3σ = 60 - 3σ

6σ = 30

σ = 5

Now we can plug this value of σ back into one of the equations for μ:

μ = 30 + 3σ

μ = 30 + 3(5)

μ = 45

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