In a volcano, erupting lava flows continuously through a tube system about 13 kilometers to the sea. Assume a lava flow speed of 0.5 kilometer per hour and calculate how long it takes to reach the sea.

Answer: 122 ft

Step-by-step explanation:

s = r Ф   (Ф must be in radians)

Given: r = 50

          Ф = 140°

                 [tex]\dfrac{\pi}{180^o}=\dfrac{x}{140^o}[/tex]  

                 [tex]\dfrac{140^o\pi}{180^o}=x[/tex]

                     [tex]\dfrac{7\pi}{9}=x[/tex]

[tex]s=50\bigg(\dfrac{7\pi}{9}\bigg)\\\\\\.\quad =\dfrac{350\pi}{9}\\\\\\.\quad =122\ ft[/tex]

Numbers 1 and 2 are correct.

Question 3:

We can see in each figure, the number of rows matches the figure amount. For example, figure 1 has 1 row, figure 2 has 2 rows, figure 3 has 3 rows, etc. Another thing we can see is that one block gets added to each column in every figure. If we count starting from 3 and keep adding 1 for each column, we get 22 blocks for one column. In figure 20, there will be 20 rows and 22 columns. We also have to keep in mind that they add 2 extra blocks at the top and bottom that stick out like the ones shown. In total, figure 20 will consist of 442 blocks.

Question 4:

[(2 + f) * (f)] + 2 = b

(2 + f) represents the number of blocks in each column.

(f) represents the number of blocks in each row.

2 represents the two extra blocks in each figure.

Note that f in this equation equals the number of the figure. For example, figure 3 is f = 3

We can test our equation with figure three.

[(2 + f) * (f)] + 2 = b

We have figure three so f = 3. Substitute and solve.

[(2 + 3) * (3)] + 2 = b

[5 * 3] + 2 = b

15 + 2 = b

17 = b

In the example, the number of blocks is 17. Therefore, this equation works for any figure.

Best of Luck!

Answer:

We will see that the number of rows in each figure corresponds to the figure amount. Figure 1 has one row, figure 2 has two rows, figure 3 has three rows, and so on. Another thing we can see is that in each diagram, one block is attached to each column. We get 22 blocks for one column if we count from 3 and keep adding 1 for each column. There will be 20 rows and 22 columns in Figure 20. We must also remember that they add two additional blocks at the top and bottom that protrude like the ones shown. Figure 20 will have a limit of 442 blocks.

4th question:

[(2 + f) * (f)] [(2 + f) * (f)] [(2 + f) 2 + 1 = b

The number of blocks in each column is represented by (2 + f).

The number of blocks in each row is represented by (f).

We will see that the number of rows in each figure corresponds to the figure amount. Figure 1 has one row, figure 2 has two rows, figure 3 has three rows, and so on. Another thing we can see is that in each diagram, one block is attached to each column. We get 22 blocks for one column if we count from 3 and keep adding 1 for each column. There will be 20 rows and 22 columns in Figure 20. We must also remember that they add two additional blocks at the top and bottom that protrude like the ones shown. Figure 20 will have a limit of 442 blocks.

4th question:

[(2 + f) * (f)] [(2 + f) * (f)] [(2 + f) 2 + 1 = b

The number of blocks in each column is represented by (2 + f).

The number of blocks in each row is represented by (f).

Steps to solve:

3(5x - 8) = 6x + 39

~Distribute left side

15x - 24 = 6x + 39

~Add 24 to both sides

15x = 6x + 63

~Subtract 6x to both sides

9x = 63

~Divide 9 to both sides

x = 7

Best of Luck!

Answer: Kukui (Hawaii) has the greater average rainfall than Melchior (Antarctic Peninsula) by 8,099.2 millimetres.

Step-by-step explanation:

Given: The average rainfall amounts for two of the world's wettest places:

Kukui (Hawaii): 9,293 millimetres              

Melchior (Antarctic Peninsula): 47 inches

Since 1 inch = 25.4 millimetres

∴ 47 inches = 47 × 25.4 millimetres

= 1193.8 millimetres

i.e. Melchior (Antarctic Peninsula) has 1193.8 millimetres of average rainfall.

Clearly,  9,293 millimetres> 1193.8 millimetres

So, Kukui (Hawaii) has the greater average rainfall .

Difference = 9293 - 1193.8 = 8099.2 millimetres

So Kukui (Hawaii) has the greater average rainfall than Melchior (Antarctic Peninsula) by 8,099.2 millimetres.

Complete question is;

Write inequalities to represent the situations below. The temperature inside the lab refrigerator is no more than 45 °F. Use t to represent the temperature (in °F) of the refrigerator.

Answer:

t ≤ 45 °F

Step-by-step explanation:

We are told to use t to represent the temperature (in °F) of the refrigerator.

We are also told that the temperature inside the lab refrigerator is no more than 45 °F.

For the temperature inside the refrigerator to be no more than 45 °F, it means the temperature should be either less than or equal to 45 °F

Thus means that t is less than or equal to 45 °F.

Thus, it can be represented in terms of inequality as;

t ≤ 45 °F

Answer:

t ≤ 35

Step-by-step explanation:

I took the test, it was right! :)

Answer:

x = 0

Step-by-step explanation:

x (40 °) ((3 x + 10) °)

40 x (3 x + 10) °^2

Expanded form:

120 x^2 °^2 + 400 x °^2

Roots:

x = -10/3

x = 0

Alternative forms:

40/3 (3 x + 5)^2 °^2 - (1000 °^2)/3

x (120 x °^2 + 400 °^2)

1/810 π^2 x (3 x + 10)

Geometric figure:

Parabola

HOPE I HELPED!

Answer:

The constant in an algebraic expression is the number part of the expression for example.. IN 2x 2 is the constant it doesn't change and x is variable it may vary

Answer:

D. 40

Step-by-step explanation:

The greater the interquartile range of a data set, the greater the variability.

Interquartile range = third quarter (Q3) - first quartile (Q1)

Interquartile range of City A = 70 - 40 = 30

Interquartile range of City B = 80 - 40 = 40.

City B has a greater interquartile range than city A, therefore, City B has the greater variability in temperature, with an interquartile range of 40.

Answer:125-1/3 can be written as : none of these

Step-by-step explanation:

(AUB)={1,2,3,4,6 }

(AUB)nC={1,2,3,4 }

The element of the set is (AUB)’ n C= { 5}

From the information given, we have that the sets are;

U ={1,2,3,...,6}

A={1,3,4,6}

B={1,2,3}

C={1,2,3,4,5}

Now, we have to take note of the following;

From the information given, we then have;

A. (AUB) = { 1, 2, 3, 4, 6}

(AUB)' = { 5}

c = {1, 2, 3, 4, 5}

Then,  the set;

(AUB)’ n C= { 5}

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Answer:

6666666666/100000000000

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

c=15×15+8×8

c=225+64

c=289=17

Answer:

The length of the guy wire is 17ft.

Step-by-step explanation:

[tex]c = \sqrt{a^{2}+b^{2} }[/tex]

a = 15ft

b = 8ft

c = [tex]\sqrt{15^{2} + 8^{2} }[/tex]

c = [tex]\sqrt{225 + 64}[/tex]

c = [tex]\sqrt{289}[/tex]

c = 17

The length of the guy wire is 17ft.

Answer:

If x = 0, then f(0) = -15

If f(x) = 27, then x = 3

Answer:

[tex]f(3)=30[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=4x^2-6[/tex]

To find f(3), substitute 3 for x. Thus:

[tex]f(3)=4(3)^2-6[/tex]

Square:

[tex]f(3)=4(9)-6[/tex]

Multiply:

[tex]f(3)=36-6[/tex]

Subtract:

[tex]f(3)=30[/tex]

And we're done!

Answer:

Step-by-step explanation:

There is a relationship between the degree of the polynomial and the number of times its graphed curved changes direction> this change is called turning point which is a point where the graph changes from increasing to decreasing or from decreasing to increasing

A polynomial of n degree will have n-1 turning points

ex: f(x)=x³+3x²+x+1

degree of polynomial is 3, it has 2 turning points (3-1)

Answer:

x-int: (-1.5, 0) and (3.5, 0)

y-int: (0, 3)

Increasing Interval: [-2, 1)

Decreasing Interval: (1, 4]

Constant Interval: [-4, -2)

Maximum: (1, 5)

Minimum: (4, -1) or (-4, -1) or (-2, -1) or (-3, -1)

Domain: [-4, 4]

Range: [-1, 5]

Step-by-step explanation:

x-intercepts are where the function f(x) crosses the x-axis when y = 0.

y-intercepts are where the function f(x) crosses the y-axis when x = 0.

Increasing interval is the set of x-values in which the graph f(x) increases in y-value.

Decreasing interval is the set of x-values in which the graph f(x) decreases in y-value.

Constant interval is the set of x-values in which the graph f(x) y-values stay constant.

Maximum is the largest y-value function f(x) can output.

Minimum is the smallest y-value function f(x) can output.

Domain is the set of x-values that can be inputted into function f(x).

Range is the set of y-values that can be outputted from function f(x).

Answer:

x^8

Step-by-step explanation:

Answer:

[tex]x^8[/tex]

Step-by-step explanation:

[tex](x^4)^2[/tex]

To solve, we will have to multiply [tex](x^4)*(x^4)[/tex] .

[tex](x^4)*(x^4)[/tex]

Now we have to multiply x.

[tex](x*x*x*x)*(x*x*x*x)[/tex]

Let's remove the parenthesis and multiply x all together.

[tex]x*x*x*x*x*x*x*x[/tex]

We multiplied x 8 times so your answer is

[tex]x^8[/tex]

Hope this helps!

The correct answer is 16737 mg

Explanation:

The first step to solve this problem is to convert the weight to kilograms because the dosage of the antibiotic is given in milligrams per kilo. This can be done by multiplying the pounds by 0.453 considering each pound is equal to 0.453 kilos. The process is shown below:

123 lb x 0.453 = 55.791 kg

Now, simply multiply the kilos by the recommended dose:

55.791 kg x 300 mg/kg = 16737 mg

Also, this can be converted to grams by dividing the number into 1000 (1000 mg = 1 g)

16737mg ÷ 1000 =  16.737 grames

Answer:

3

Step-by-step explanation:

Simplifying

5x + -2 = 3x + 4

Reorder the terms:

-2 + 5x = 3x + 4

Reorder the terms:

-2 + 5x = 4 + 3x

Solving

-2 + 5x = 4 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

-2 + 5x + -3x = 4 + 3x + -3x

Combine like terms: 5x + -3x = 2x

-2 + 2x = 4 + 3x + -3x

Combine like terms: 3x + -3x = 0

-2 + 2x = 4 + 0

-2 + 2x = 4

Add '2' to each side of the equation.

-2 + 2 + 2x = 4 + 2

Combine like terms: -2 + 2 = 0

0 + 2x = 4 + 2

2x = 4 + 2

Combine like terms: 4 + 2 = 6

2x = 6

Divide each side by '2'.

x = 3

Simplifying

x = 3

A rational number means it doesn't have a decimal that repeats. For example, 2/3 or 0.66....

There is only one number between 9.5 and 9.7. This number is 9.6.

The decimal doesn't repeat or go on forever so its rational.

Answer: 9.6

Best of Luck!

Answer:

9.6

Step-by-step explanation:

decimals are rational so ye

Answer:

158,400

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-5, 4) and (0, 0)

(0 - 4)/(0 + 5) = -4/5

y - 4 = -4/5(x + 5)

y - 4 = -4/5x - 4

y = -4/5x

Answer:

[tex]x = 1.2[/tex]

See Attachment for Graph

Step-by-step explanation:

Given

[tex]y = -x + 4[/tex]

[tex]y = 4x - 2[/tex]

Required

Determine the point of intersection

To do this, we simply equate both expressions of y

i.e.

[tex]-x + 4 = 4x - 2[/tex]

Solve for x

[tex]-x - 4x = - 2 - 4[/tex]

[tex]-5x = -6[/tex]

Divide through by -5

[tex]x = \frac{-6}{-5}[/tex]

[tex]x = \frac{6}{5}[/tex]

[tex]x = 1.2[/tex]

Hence, the point of intersection is 1.2

Answer:

50$

Step-by-step explanation:

25 percent more means 1 and 1/4 of original price

aka 5/4

(5/4)(40)

50

OR

1/4 of 40 is 10

10 plus 40 is 50

Answer:

Step-by-step explanation:

[tex]Original \:price =\$40\\Percentage\:increase =25\%\\\\\frac{25}{100} \times 40\\\\= \frac{1000}{100} \\\\= \$10\\\\New\:price = \$40 +\$10\\= \$50[/tex]

Answer:

The Factor is 1.5

Step-by-step explanation:

5.1(which is B'C') divided by 3.4(which is BC) = 1.5

3.6(A'C') divided by divided by 2.4(AC) = 1.5

2.7(A'B') divided by 1.8(AB) = 1.5

Henceforth the factor is 1.5  

Answer:

[tex]16[/tex]

Step-by-step explanation:

[tex]2^4[/tex]

To solve, you're gonna have to multiply 4 times.

[tex]2*2*2*2[/tex]

[tex](2*4)(2*4)[/tex]

Since [tex]4*2[/tex] is [tex]8[/tex] , you will have to multiply [tex]8[/tex] by [tex]2[/tex].

[tex]8*2=16[/tex]

Your answer is [tex]16[/tex].

Hope this helps!

Answer:

the correct answer is B.

Answer:

15.9% of the data will be greater than 235.3.

Step-by-step explanation:

Use a calculator with statistical functions.  In this case you'll need the cumulative normal distribution:  normcdf(.

Evaluate the following:  normcdf(235.3, 10000,186.4, 48.9):

We get:  0.159, or 15.9%

15.9% of the data will be greater than 235.3.

The range of value X > 284.2 of data will be greater than 235.3.

A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores.

We know that the upper 2.5% of data would be 97.5% of data.

We will use a z-score formula to solve our given problem.

[tex]\rm z=\dfrac{x-\mu}{\sigma}[/tex]

Where; z = z-score,

x = Random sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation.

We will use a normal distribution table to find a z-score corresponding to 97.5% area or 0.975.

We can see from the normal distribution table that the z-score corresponding to the area of 0.975 is 1.96.

[tex]\rm 1.96=\dfrac{x-186.4}{48.9}\\\\1.96 \times 48.9 =x-186.4\\\\x = 186.4 +95.84\\\\x=282.84[/tex]

Hence, the range of value X > 284.2 of data will be greater than 235.3.

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Answer:

b) in the vertex.

Step-by-step explanation:

In the vertex. If the parabola opens up or down the axis of symmetry is x = a where a is the x coordinate of the vertex.

If it opens to the left or right the axis is y = a where a is the y-coordinate if the vertex.