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The equation of the Damari's investment is B(x) = 30000 * 1.03ˣ

Damari's investment

Given that

Initial value, a = 30000

B(3) = 32306.72

The function is calculated as

B(x) = a * bˣ

Using B(3), we have

30000 * b³ = 32306.72

So, we have

b³ = 1.077

Take the cube root of both sides

b = 1.03

So, we have

B(x) = 30000 * 1.03ˣ

So, the function is B(x) = 30000 * 1.03ˣ

The boat of Sky's family

Here, we have

Initial value = 6000

Rate of depreciation = 6%

So, the function is

f(x) = 6000 * (1 - 6%)ˣ

So, we have

f(x) = 6000 * (0.94)ˣ

In 2024, we have

x = 2024 - 2021

x = 3

So, we have

f(3) = 6000 * (0.94)³

Evaluate

f(3) = 4983.50

This value is less than the offered value of $5000

This means that Sky's family should take the offer

The rule of the function

Here, we have the graph

From the graph, we have

Initial value, a = 8

Rate, b = 4.8/8

So, we have

Rate, b = 0.6

So, the function is

f(x) = 8 * 0.6ˣ

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Answer:

R500

Step-by-step explanation:

20 books x R25 each = R500.

The value of number of students who failed in both mathematics and English is 40.

Since, Given that;

60% of the 1000 students passed the examination,

Hence, we can calculate the number of students who passed the exam as follows:

60/100 x 1000 = 600

So, 600 students passed the examination.

Now, let's find the number of students who failed the examination.

Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:

40/100 x 1000 = 400

Of the 400 failing students, we know that 60% failed in mathematics.

So, the number of students who failed in mathematics is:

60/100 x 400 = 240

Similarly, we know that 50% of the failing students failed in English.

So, the number of students who failed in English is:

50/100 x 400 = 200

Now, we need to find the number of students who failed in both subjects.

We can use the formula:

Total = A + B - Both

Where A is the number of students who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.

Substituting the values we have, we get:

400 = 240 + 200 - Both

Solving for Both, we get:

Both = 240 + 200 - 400

Both = 40

Therefore, the number of students who failed in both mathematics and English is 40.

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Answer:

24 cakes.

Step-by-step explanation:

6 cups of oil divided by 1/4 cup oil per cake = 24 cakes

6/(1/4) = 24

or 6/(0.25) = 24

She can make 24 cakes with 6 cups of oil.

The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

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1. Event A includes the outcomes of H and T,

2. while event AC includes all the possible outcomes of rolling a number cube, which are 1, 2, 3, 4, 5, and 6.

1. Event A is defined as tossing a heads on a coin, regardless of the outcome of rolling a number cube. Therefore, the outcomes in event A are H (heads) and T (tails), since either of these outcomes could occur when rolling a number cube and tossing a coin.

2. Event AC is the complement of event A, i.e., it is the set of outcomes that are not in event A. Since event A contains H and T, the outcomes in event AC are the remaining outcomes that are not in event A, which are all the possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, and 6.

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Answer:

20

Step-by-step explanation:

She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.

The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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The critical values t₀ for a two-sample t-test is ± 2.0.6

To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:

t₀ = ± t_(α/2, df)

where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.

The degrees of freedom are calculated as:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8

α = 0.05 (two-tailed)

First, we need to calculate the degrees of freedom:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]

= 24.27

Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.

From a t-distribution table, we find:

t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)

Finally, we can calculate the critical values t₀:

t₀ = ± t_(α/2, df) = ± 2.0639

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