Predict: How do you think the formula for area of a triangle will relate to the formula for area of a rectangle? Do you
think it is the same area formula?

Answer:

12 gallons in 6 min

Step-by-step explanation:

4 gallons in 2 min

? gallons in 6 min

4 x 6 / 2

24/2 = 12

12 gallons in 6 min

Answer:

  (d)  59 ft

Step-by-step explanation:

In the geometric model of the problem, the guy wire is the hypotenuse of a right triangle, with the tower being one leg, and the distance along the ground from the tower being the other leg. The ground distance is "adjacent" to the angle of elevation, so the relevant trig function is ...

  Cos = Adjacent/Hypotenuse

Solving for the hypotenuse, gives ...

  hypotenuse = adjacent/cos(α) = (34 ft)/cos(55°) ≈ 59 ft

The length of the guy wire is about 59 feet.

Answer:

4 and -2

Step-by-step explanation:

4 + -2 = 2

4 x -2 = -8

Answer: 12.5

Step-by-step explanation:

So, basically there is 5 minutes and the number of times occuring is 5 so its 5x1 which is 5 and then there is 10 minutes and the number of times occuring  is twice so its 2x10 which is 20. Next, is 15 minutes and the times occuring  is 2 so, 2x15 which is 30. And finally theres  20 minutes and the amount of times occuring  is once so 20x1 which is 20. Then you add them all up which is 5+20+30+20=75. And the formula for mean/average is The sum of all number/ The amount of numbers there are so 75/6 is 12.5.

Answer:

If you don't agree or there's an error, let me know so I can edit.

Step-by-step explanation:

f(x) = x⁴ + 2

differentiate

f(x) = 4x³ + 0 =0

x(4x²) = 0

at x= 0 f(x) = 0 points = (0,0)

at x= 1. f(x) = 3 points = (4,3)......

The ordered pair is (4,3).

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.

Given:

f(x) = x⁴ + 2

Now, differentiate the above function for the small values

f(x) = 4x³ + 0 =0

x(4x²) = 0

When x= 0

f(x) = 0

So, the points = (0,0)

when x= 1

f(x) = 3

so, the points = (4,3).

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Answer:

\( \sqrt{6} \)

Step-by-step explanation:

\( \sin \: 45 \degree = \frac{ \sqrt{3} }{x} \\ \\ \frac{1}{ \sqrt{2} } = \frac{ \sqrt{3} }{x} \\ \\ x = \sqrt{2} \times \sqrt{3} \\ \\ x = \sqrt{2 \times 3} \\ \\ x = \sqrt{6} \)

Answer:

√6

Step-by-step explanation:

Find the length of side x in simplest radical form with a rational denominator.

√6

The sum of measures of all the interior angles in the polygon having 30 sides​ is 5040°.

A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry. The interior and exterior angles of regular and irregular polygons are related by polygonal angles.

The angles found inside a polygon with two sides are called interior angles. By deducting 2 from the total number of sides and multiplying by 180°, we may find the sum of the interior angles of a polygon.

Sum of Interior Angles = (n-2) × 180°

n = 30

So, the Sum of Interior Angles = (30-2) × 180° = 28 × 180° = 5040°

Thus, the polygon's 30 sides add up to a total interior angle measure of, 5040°.

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As per the FIFO algorithm, there have been a total of 13 page faults.

The FIFO algorithm is a page replacement strategy used in operating systems to manage the allocation of memory frames to pages.

For the given reference string of

=> 1, 2, 3, 4, 5, 3, 4, 1, 6, 7, 8, 7, 8, 9, 7, 8, 9, 5, 4, 5, 4, 2

with four-page frames, we can see that there will be multiple page faults. Initially, all four frames are empty, so there will be four page faults as the first four pages are brought into memory.

Then, when page 5 is needed, the oldest page in memory, page 1, is replaced leading to another page fault.

As the reference string continues, there are several page faults that occur as pages are replaced

By the end of the reference string, there have been a total of 13 page faults.

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Answer:

yes

Step-by-step explanation:

-32/8 = -4

-4 is an integer

Answer:

Part A) x = -3

Part B) x = 1, x = -7

Part C) x < -7

Part D) 2

Step-by-step explanation:

2(x - 3) = 3x - 3

open the parenthesis

2 * x - 2 * 3 = 3x - 3

2x - 6 = 3x - 3

subtract 2x from both sides

2x - 2x - 6 = 3x - 2x - 3

-6 = x - 3

add 3 to both sides

-6 + 3 = x

-3 = x

|2x + 6| = 8

split this into two equations:

2x + 6 = 8

&

2x + 6 = -8

2x + 6 = 8

2x = 8-6

2x = 2

x = 1

2x + 6 = -8

2x = -8 - 6

2x = -14

x = -7

-5(x + 1) > 30

open the parenthesis

-5x - 5 > 30

add 5 to both sides

-5x > 35

divide both sides by -5

x > -7

since you divided by a negative, flip the sign.

x < -7

f(x) = 4x - 3

substitute x for 5

5 = 4x - 3

5 + 3 = 4x

8 = 4x

2 = x

use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

Answer:

390 Mins

Step-by-step explanation:

If we take a look here, we currently have 600 total mins, and we are trying to find the total time that he spends on OTHER homework besides math

we know that he spends 35% of his time on math, so let's take the difference to find the percentage of time spent on other assignments

100%-35% = .65

Now that we know the percentage of time he spends on other work, we find the amount of time he spends on those other assignments by multiplying the total by the percentage

600*.65 = 390 mins

Answer:

The answer is option 2.

Step-by-step explanation:

You have to apply Logarithm Laws :

\( ln( a) - ln(b) ⇒ ln( \frac{ a}{b } ) \)

\( ln( {x}^{2} ) ⇒2 ln(x) \)

For this question :

\( ln( \frac{ {x}^{2} }{18} ) \)

\( = ln( {x}^{2} ) - ln(18) \)

\( = 2 ln(x) - ln(18) \)

Answer:

It will take 10 minutes to fill the tank completely.

Step-by-step explanation:

If the 30-gallon tank already has 3 gallons of water in it, then 27 more are needed to fill the tank.  Thus, at time t = 0, g(0) = 3 gallons, and

g(t) = (3 gallons) + (2.7 gal/min)t, where t is the time in minutes.

At the time the tank is completely full, it holds 30 gallons.  How long does this take to achieve:  Set (3 gallons) + (2.7 gal/min)t equal to 30 gallons:

30 = 3 + 2.7t, or 27 = 2.7t, or t = 10 minutes

It will take 10 minutes to fill the tank completely.

The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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Answer:

They are supplementary angles.

Step-by-step explanation:

161+ 19 = 180

When two angles add to 180 degrees, they  are supplementary angles

Answer:

Supplementary Angles

Step-by-step explanation:

They add to 180 degrees

The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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Answer:

b

Step-by-step explanation:

I think I know but I dont think it's going to be the right answer. But good luck anyway!

Answer:

4(7w+10)

Step-by-step explanation:

Answer:

4(7w+10)

Step-by-step explanation:

5(3x-6) is equivalent to 15x - 30 if they are equivalent if the two values are the same.

An expression is a set of terms combined using the operations +, – , x or , /.

Given expression:

5(3x-6) is equivalent to 15x - 30.

If we put x=2 in both expression, we get finite value.

To check both the expression are equal or not we have to solve by putting the value.

So,

They are equivalent if the two values are the same otherwise not.

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It is possible to use a relational operator and math operators in the same expression.

In programming, you can use relational operators (e.g., <, >, ==, !=) and math operators (e.g., +, -, *, /) together in the same expression. This is often used in conditional statements or loops to compare calculated values.

For example, consider the following expression:

`if (2 * 3) > (4 + 1)`

In this expression, we have math operators (*) and (+) and a relational operator (>). The math operations are evaluated first, resulting in:

`if (6) > (5)`

Then, the relational operator (>) is evaluated, and the expression becomes:

`if True`

The expression is true because 6 is greater than 5.

It is possible to use both relational operators and math operators in the same expression, which can be useful in various programming situations such as conditional statements or loops.

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No, it doesn't show that single individuals under the age of 25 have more insurance claims than the nationwide percent reported by the big insurance firm.

Hypothesis

Null hypothesis : H0: p = 0.68

Alternative hypothesis : Ha: p > 0.68

A random sample of 53 claims showed that 41 were made by single people under the age of 25.

Thus; p^ = 41/53 = 0.7736

The test statistic is

z = (p^ - p_o)/√(p_o(1 - p_o)/n)

z = (0.7736 - 0.68)/√(0.68(1 - 0.68)/41)

z = 0.0936/0.07285

z = 1.28

The p-value from z-score calculator, using z = 1.28, one tail hypothesis and significance level of 0.05,we have;

P(z > 1.28) = 0.100273

The p-value gotten is greater than the significance value and so we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

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Answer:

It's actually: None of these.

Think about it: In this case we have an inequality, of x ≤ 0.

This basically means, that x can be less than OR equal to 0.

But 0 is neither negative or positive, so we can eliminate the following answer choices:

- all positive integers

- all negative real numbers

- all positive real numbers

- all negative integers

And we are left with "None of these"

Let me know if this helps!

Option B is correct. None of these options is the right answer since zero is neither an integer nor a real number

Before we can decide which option is correct, first we must integers and real numbers are.

Given the set of numbers {x | x ≤ 0}. The set of numbers in the set will be all integers less than zero including zero (zero is not an integer)

Hence the set of numbers are not all negative integers since 0 is not a negative integer.

They are not all positive integers rather they are mostly negative integers

They are not all positive and negative real values because zero is not a real integer.

Hence we can conclude that None of the options is correct.

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Answer:

V = 54 pi in ^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = pi (3)^2 * 6

V = pi (9) *6

V = 54 pi in ^3

Answer:

x^2 - x - 6 = 0

Step-by-step explanation:

If the quadratic equation has solutions 3 and -2, then it can be factored as:

(x - 3)(x + 2) = 0

Expanding the left side of the equation, we get:

x^2 - x - 6 = 0

This is the quadratic equation that has a leading coefficient of 1 and solutions 3 and -2.

To determine the appropriate significance level for performing a significance test based on the confidence level used to construct the confidence interval,

we need to consider the relationship between confidence level and significance level.

The confidence level represents the probability that the confidence interval will contain the true population parameter. In this case, the confidence level was not provided, so we cannot directly determine the significance level based on the given information.

Typically, a 95% confidence level is commonly used, which corresponds to an alpha (significance level) of 0.05. This means that there is a 5% chance of rejecting the null hypothesis when it is true.

However, it is important to note that the specific significance level to be used in a significance test should be determined in advance based on the requirements of the study, the consequences of Type I and Type II errors, and any relevant guidelines or standards in the field of study. The coach or researcher conducting the study should define the significance level based on these considerations.

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Answer:

C=2 x pi x radius

Step-by-step explanation:

Answer:

140 adults.

Step-by-step explanation:

5:7 Ratio. 100 Children, so if we want the adults we want to reverse the ratio, 100 x 7/5 = 140.  

140 Adults.

To check our work we can see if the fractions are the same, so divide 5/7 and 100/140 and you'll see they both have the same result.