The height of lava fountains spewed from volcanoes cannot be measured directly. Instead, their height in meters
can be found using the equation
1
where y represents the height, g is 9.8, and t represents the falling time of the lava rocks. Find the height in
meters of a lava rock that falls for 5 seconds.

Answer:

cosJ ≈ 0.38

Step-by-step explanation:

This is a 5- 12- 13 right triangle

with HI = 12, HJ = 13, IJ = 5

cosJ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{IJ}{HJ}\) = \(\frac{5}{13}\) ≈ 0.38 ( to nearest hundredth )

The required value of Cos(J) for the given triangle is 0.38.

Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².

In the given ΔHIJ the sides are given as,

JH = 13  and HI = 12.

Now, apply Pythagoras theorem to obtain,

IJ² + HI² = JH²

⇒ IJ² = 13² - 12²

⇒ IJ = 5

Use trigonometric ratio to obtain,

Cos(J) = IJ/HI = 5/13 = 0.38

Hence, the value of Cos(J) is obtained as 0.38.

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The sum of the shares of seun and dayo is n80.00.

A ratio shows how frequently a number encompasses another. If you have eight oranges and six lemons in a fruit plate, the orange-to-lemon ratio is eight to six. Similarly, the orange-lemon ratio is 6:8, and the orange-to-total fruit ratio is 8:14.

Given that,

Seun, tayo and dayo are to share n = 120 in the ratio 4:3:2 respectively.

Here n = 120

Seun ,tayo and dayo = 4:3:2

Seun shares = 120 × \(\frac{4}{9}\)

seun shares = 120 × 0.44

seun shares = 53.33

dayo shares = 120 × \(\frac{2}{9}\)

dayo shares = 120 × 0.22

dayo shares = 26.67

Sum of the shares of seun and dayo is 53.33 + 26.67

Sum of the shares of seun and dayo is 80.00

Therefore, the sum of shares of seun and dayo is 80.00.

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Answer:

A my dude. good luck!!!!!

Answer:

A

Step-by-step explanation:

AC = 5

DF = 15

5 x 3 = 15

BC = 3

EF = 9

3 x 3 = 9

Do you see the pattern? So as you can see the difference between Triangle ABC and DEF is the multiply/divide 3 so if you want to find DE then you should set it up as:

\(\frac{4}{3}\) = \(\frac{DE}{9}\)  and to check if its right if you solve it you get \(\frac{4}{3}\) = \(\frac{12}{9}\)

and as you see \(\frac{12}{9}\) and \(\frac{4}{3}\) are literally the same thing just you need to simplify \(\frac{12}{9}\)

The simplified form of the expression as given in the task content is; 12.

The expression given in the task content can be simplified by means of PEMDAS guidelines as follows;

3 – (−2) + |−7|

= 3 +2 +7

= 12.

Hence the simplified form of the expression is 12.

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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The answer to the division equation is "1/6".

To solve the division equation "one-third divided by two equals blank" using the fraction model, we can represent the fraction strip as follows:

1/3

The fraction strip is partitioned into three equal parts, each of which is partitioned into two equal parts. Therefore, we have a total of 6 equal parts.

1/3 = 6/6

Out of the 6 equal parts, one part is shaded. So the shaded part can be represented as:

1/6

Hence, the equation "one-third divided by two" can be written as:

1/3 ÷ 2 = 1/6

Therefore, the answer to the division equation is "1/6".

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The relationship between the cups of juice sold and time is y = 25x

A variation is a relation between a set of values of one variable and a set of values of other variables.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

Direct variation means increase in a quantity will be increase in the other quantity and vice versa.

Direct variation is expressed in the form;

y = Kx

let x be the number of hours and y be the number of juice sold.

When 25 cups is sold for 1 hr

25 = k 1

k = 25

Therefore the relationship can be written as;

y = 25x

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Answer:

Apothem:

radius is the same length as the base/length of each side of the hexagon.

r = 8

use pythagorean theorem to calculate the apothem

\(4^2+a^2=8^2\\\\16+a^2=64\\\\a^2=48\\\\a= 6.928\)

≈ 6.9

Area

\(A = \frac{3\sqrt{3} }{2} *a^2\\\\=\frac{3\sqrt{3} }{2}(6.928)^2\\\\=124.7\)

Answer:

The product of 31 and x is 31x.

Answer:

(i) 4000

(ii) $5.00

Step-by-step explanation:

Let no. of shares of Company A be X

Let share price of Company B on Day 7 be $y

Share price of Company B on Day 12 = $(y-0.50)

(i)

Consider Day 7:

4.60x - 2000y = 7400................ (1)

Consider Day 12:

4.80x - 5000(y-0.50) = -5800

4.80x - 5000y + 2500 = -5800

4.80x - 5000y = -8300............... (2)

(1)*2.5:

11.5x - 5000y = 18500................. (3)

(3)-(2):

11.5x - 4.80x - 5000y + 5000y = 18500 + 8300

6.70x = 26800

x = 4000

(ii)

Sub. x = 4000 into (1):

4.60(4000) - 2000y = 7400

-2000y = 7400 - 18400

-2000y = -11000

y = 5.5

Share price of Company B on Day 12

= 5.50 - 0.50

= $5.00

Given the graph,

We can find the range of the graph by taking note of the set of all y values, the dependent quantity, that will result from substituting all x values (the domain) into the function.

To do this we would look at the graph and note all the range of values that correspond to the y axis.

This then gives the range of values to be;

This is because, A which is one end of the range indicates -3, and is shaded(less than or equal to) and E which is another end of the range indicates +3 and is not shaded(strictly less than).

Therefore, the answer is;

Answer: Option 1

The outside of an apple seed is coated with a protective layer called the seed coat. This hard, outer layer is designed to protect the inside of the seed from damage, disease, and pests. The seed coat also helps

Regulate the moisture levels within the seed, ensuring that it doesn't dry out or become too wet. As the apple tree grows, it produces fruit that is eaten by animals. When animals eat the apple, they consume the entire fruit, including the core and seeds. The seed coat protects the seeds as they pass through the animal's digestive system, ensuring that they remain intact and ready to germinate once they are excreted.

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The question is incomplete, the complete question is:

A simple random sample of size n from a finite population of size n is a sample selected such that each possible sample of size the same probability of being selected.

As we know that,

A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling. Every person in the population has the same chance of being chosen.

So n has the same probability of being selected.

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The right question is

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size

n has a probability of 0.5 of being selected.

n has the same probability of being selected.

N and n have the same probability of being selected.

n has a probability of 0.05 of being selected.

The account's balance after 5 years is given as follows:

\(A(5) = P\left(1 + \frac{r}{4}\right)^{20}\)

In which:

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

Quarterly compounding means that the value of n is given as follows:

n = 4.

Then the balance of the account after 5 years, when t = 5, is given as follow:

\(A(5) = P\left(1 + \frac{r}{4}\right)^{20}\)

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Answer:

12 nickels : 15 pennies =

4 nickels : 5 pennies

Answer: 12:15

Step-by-step explanation: if the nickels are 12 and penies are 15 the when an question ls the opposite side then just switch the numbers around.

The provided C++ expressions represent the algebraic expressions using the appropriate syntax in the programming language, allowing for computation and assignment of values based on the given formulas.

Here are the C++ expressions for the given algebraic expressions:

1. yaygy = 6 * x

```cpp

int yaygy = 6 * x;

```

2. x = 2 * b + 4 * c

```cpp

x = 2 * b + 4 * c;

```

3. x3 = z²

```cpp

int x3 = pow(z, 2);

```

Note: To use the `pow` function, include the `<cmath>` header.

4. z2x+2 = z²x²

```cpp

double z2xplus2 = pow(z, 2) * pow(x, 2);

```

Note: This assumes that `z` and `x` are of type `double`.

Make sure to declare and initialize the necessary variables (`x`, `b`, `c`, `z`) before using these expressions in your C++ code.

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Complete Question:

Write C++ expressions for the following algebraic expressions

Answer: M'=(-2,3)

Step-by-step explanation:

Rotation of point through 90° about the origin in anticlockwise direction when point M (h, k) is rotated about the origin O through 90° in anticlockwise direction. The new position of point M (h, k) will become M' (-k, h).

For this h=3, and k=2 so the new point will be M'=(-2,3)

The triangle has height 4.6 mm and its base has length 3.4 mm, so its area is

1/2 • 4.6 mm • 3.4 mm = 7.82 mm²

The length of the third side of the triangular garden is 30 meters.

Let,

The length of the third side = x

The length of the first side = 28 meters

The length of the second side = 43 meters

The perimeter of the triangular garden = 101 meters

The perimeter is the sum of the measures of all the sides of a figure.

Perimeter = sum of the three sides of the triangle

Perimeter = 28+43+x

Substitute perimeter=101:

101 = 28+43+x

101 = 71+x (simplify)

30 = x (subtract 71 on both sides of the equation)

Therefore, the triangular garden will have a length of 30 meters if the perimeter is 101 meters.

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The value of the 10% trimmed mean is approximately 1.3027. To calculate the 10% trimmed mean, we need to trim off the lowest and highest 10% of the data and then find the mean of the remaining values.

First, let's sort the data in ascending order:

0.2, 0.21, 0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26, 3.06, 3.24

Next, we calculate the number of values to trim from each end:

10% of 15 (total number of values) = 0.1 * 15 = 1.5

Since we can't remove half a value, we round up to the nearest whole number, which is 2.

Now, we remove the two lowest and two highest values:

0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26

Finally, we calculate the mean of the remaining values:

(0.26 + 0.3 + 0.33 + 0.41 + 0.54 + 0.57 + 1.41 + 1.7 + 1.84 + 2.2 + 2.26) / 11 = 14.33 / 11 ≈ 1.3027

Rounding to four decimal places, the value of the 10% trimmed mean is approximately 1.3027.

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Answer:

,bn ljb ib

Step-by-step explanation:

Answer:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

Step-by-step explanation:

Swap f(x) and x position of the function, thus:

\(\displaystyle{x=7f(x)+3}\)

Then solve for f(x), subtract 3 both sides and then divide both by 7:

\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)

Since the function has been inverted, therefore:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

And we can prove the answer by substituting x = 1 in f(x) which results in:

\(\displaystyle{f(1)=7(1)+3 = 10}\)

The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):

\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)

The input is 1. Hence, the solution is true.

8 additional workers need to be added for the remaining 6 days to complete the graduation task. The remaining work to be done is 7/12.

Let's solve the problem step by step:

We are given that 15 workers can complete the graduation task in 12 days. On the morning of the 5th day, the task is already partly completed.

To determine the progress made by the morning of the 5th day, we can calculate the total work done up to that point. Since the workers are equally efficient, we can assume that the work is distributed evenly over the days.

From day 1 to day 5, a total of 5 days have passed. Since the workers are completing the task in 12 days, the progress made by the morning of the 5th day is 5/12 or 5/12th of the total work.

Therefore, the remaining work to be done is 1 - (5/12) = 7/12.

To complete the remaining work in the remaining 6 days, x workers are added.

Since we have established that the 15 workers can complete the task in 12 days, we can set up a proportion to determine the relationship between the number of workers and the number of days.

15 workers / 12 days = x workers / 6 days

By cross-multiplying, we get:

15 * 6 = 12 * x

90 = 12x

Dividing both sides by 12, we find:

x = 90 / 12

x = 7.5

Since the number of workers must be a whole number, we cannot have 7.5 workers. Therefore, we round up to the nearest whole number.

Therefore, x is rounded up to 8 workers.

In conclusion, 8 additional workers need to be added for the remaining 6 days to complete the graduation task.

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Answer: 23.1

Step-by-step explanation:

By the inscribed angle theorem, we know the measure of arc DC is 120 degrees. So, we can set 120=7x-42.

162 = 7x

x = 162/7, which is about 23.1

Answer: The sequence is defined by the rule f(n) = 2n^2 + 4.

To find the first 4 terms of the sequence, we need to plug in the values of n into the rule and calculate f(n) for each value of n.

n = 1: f(1) = 2(1)^2 + 4 = 2 + 4 = 6

n = 2: f(2) = 2(2)^2 + 4 = 8 + 4 = 12

n = 3: f(3) = 2(3)^2 + 4 = 18 + 4 = 22

n = 4: f(4) = 2(4)^2 + 4 = 32 + 4 = 36

So, the first 4 terms of the sequence are 6, 12, 22, 36

Step-by-step explanation:

9514 1404 393

Answer:

  x = 5

Step-by-step explanation:

Perhaps you want to solve for x the rational equation ...

  (2+5x)/(3x) = (7x -18 +2x)/(3x)

Multiplying by 3x and collecting terms, we have ...

  2 +5x = 9x -18

  20 = 4x . . . . . . add 18-5x to both sides

  5 = x . . . . . . . . divide both sides by 4

The solution is x=5.

Answer:

converse alternate exterior angles therom

Step-by-step explanation:

just took it rn

Answer:

converse alternate exterior angles theorem

Step-by-step explanation:

took the test got 100 edge 2021

Answer:

Step-by-step explanation:

LENGTHS: P, Q, R

AREAS: A, B

CODE: PLRAQB