4. Old Faithful, Yellowstone National Park's most famous
geyser, shoots a spray of steam and hot water 50 m
into the air. Is this height greater or less than 5,000 mm?

Answer:

BGHA

Step-by-step explanation:

Just look at the coordinates.

1 is at x=0 and y=4, so (0, 4), or B

2 is at x=-4 and y=3, so (-4, 3), or G

3 is at x=2 and y=0, so (2, 0), or H

4 is at x=0 and y=-1, so (0, -1), or A

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.

To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:

Step 1: Draw the angle ABC with a straightedge.

Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.

Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.

Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.

Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.

In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.

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This statement is true because when we add decimal numbers, we have to line up the digits from the last number to the first. Otherwise, the sum will be wrong.

Answer:

  2x² +5

Step-by-step explanation:

You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.

The area is the product of length and width, so the width will be ...

  A = LW

  W = A/L = (2x³ +6x² +5x +15)/(x +3)

The cubic expression can be factored by grouping, so we have ...

  Area = (2x³ +6x²) +(5x +15)

  = 2x²(x +3) +5(x +3)

  = (2x² +5)(x +3)

Then the width is ...

  \(\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}\)

The width of the rectangle is 2x² +5.

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if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25.

The concept of "1" in mathematics typically represents a whole unit or a single entity. However, your question about how many parts "1" equals to requires clarification. If you are referring to dividing a whole into parts, then "1" can be divided into any number of parts, as long as each part is equal.

For instance, if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25, and so on. In this context, "1" can be divided into an infinite number of parts, depending on the desired level of precision or subdivision.

On the other hand, if you are referring to expressing "1" as a fraction or a ratio, it can be written as 1/1 or 1:1, indicating that there is one part in total, and that one part is the whole itself.

In this case, "1" is not divided into multiple parts but represents the entirety of a single unit.

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9514 1404 393

Answer:

  (a)  145

Step-by-step explanation:

The measure of the angle marked x° is half the sum of the intercepted arcs:

  (90° +200°)/2 = x° = 145°

There are four corner points in the feasible region of the given problem.

We must first plot the system of inequalities on a graph and locate the region that fulfills all of the constraints in order to ascertain the number of corner points in the feasible zone of the given problem.

Let's analyze each constraint:

1) X ≥ 4: This is a vertical line passing through the point (4, 0) and extending indefinitely to the right.

2) -X ≥ 2: This is a vertical line passing through the point (-2, 0) and extending indefinitely to the left.

3) X + 2Y ≤ 6: This is a downward-sloping line passing through the points (0, 3) and (6, 0).

4) -X + 2Y ≤ 8: This is a downward-sloping line passing through the points (0, 4) and (8, 0).

Y ≥ 0: This represents the non-negative y-axis.

We must ascertain the area where all the limitations overlap in order to identify the viable zone.

First, we notice that the region satisfying constraint 1 (X ≥ 4) is to the right of the line.

Next, we consider constraint 2 (-X ≥ 2), which is to the left of the line.

For constraint 3 (X + 2Y ≤ 6), we shade the region below the line.

For constraint 4 (-X + 2Y ≤ 8), we shade the region below the line.

Finally, for constraint 5 (Y ≥ 0), we consider the region above the x-axis.

When we consider all the shaded regions together, we find that the feasible region is a polygon with four corners.

The corners of the feasible region are as follows:

(4, 0)

(2, 0)

(0, 3)

(0, 4)

Therefore, there are four corner points in the feasible region of the given problem.

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Answer:
30-2=28+542=570

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

45 dicided by 15 is 3 or 45 divided by 3 is 15!

Step-by-step explanation:

let Sams father's age=3x

that is 3x=45

divide both sides by the coefficient of x

3x/3=45/3

x=15

Answer:

C. (-5,-1)

E. (10,2)

F. (15,3)

------------------

hope it helps...

have a great day!!

Answer:

z=0

50%

Step-by-step explanation:

let the number of sweets with Angela be " x "

and , let the number of sweets with Sabrina be " 3x "

Then ,

\(\bold{x + 3x = 60} \\\\\bold{ 4x = 60} \\\\\bold{ x = \cancel \frac{60}{4}} \\ \\\fbox\pink{ x = 15}\)

Hence ,

number of sweets with Angela = 15

number of sweets with Sabrina = 3(15) = 45

hope helpful~

Slope = -13

The slope of a line passing through two points with coordinates (x₁ , y₁ ) and (x₂ y₂) is calculated using the formula:

Since the points are (6, 6) and (7, -7):

x₁ = 6, y₁ = 6, x₂ = 7, y₂ = -7

Substituting these into the formula:

Answer:

We use the binomial distribution to describe this situation.

The mean number of phone sales is 749.7 with a standard deviation of 15.

Step-by-step explanation:

For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.

This means that \(p = \frac{35}{50} = 0.7\)

What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day

1071 shoppers, so \(n = 1071\)

Mean

\(E(X) = 1071*0.7 = 749.7\)

Standard deviation

\(\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15\)

The mean number of phone sales is 749.7 with a standard deviation of 15.

on solving the provided question we can say that This means that as the domain speed you are driving increases, the amount of time needed to drive from city A to city B decreases proportionally.

A function's domain is the range of potential values that it can accept. These numbers indicate the x-values of a function like f. (x). The range of potential values that can be utilised with a function is known as its domain. The value that the method returns after inserting the x value belongs to this set. The formula for a function with y as the dependent variable and x as the independent variable is y = f. (x). When a single value of y can be successfully produced from a value of x, that value of x is said to be in the domain of the function.

The relationship between the amount of time needed to mow a yard and the size of the yard is an example of a direct variation. This means that as the size of the yard increases, the amount of time needed to mow the yard increases proportionally.

II. The relationship between the amount of time needed to drive from city A to city B and the speed you are driving is an example of an inverse variation. This means that as the speed you are driving increases, the amount of time needed to drive from city A to city B decreases proportionally.

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Answer:

7:13

5:8

Step-by-step explanation:

Do 13 minus 5 and that is number of red apples. So the ratio is 8 to 13 total apples. So there are 5 green apples and 8 red apples so it’s going to be 5:8

Answer:

a = -3

:)))))))))))))))

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

$1,200 interest.

Step-by-step explanation:

To use the simple interest formula, I = Prt, we substitute in the values for variables that are given, ... Do you know that banks pay you to let them keep your money? ... Find the rate if a principal of $9,000 earned $1,755 interest in 3 years. ... Five years later, she paid him back the $8,000, plus $1,200 interest.

Answer:

6

Step-by-step explanation:

Given problem:

Therefore:

\(\implies \dfrac{12}{2(-1)+4}\)

Multiply the 2 and -1 in the denominator first:

\(\implies \dfrac{12}{-2+4}\)

Now carry out the addition in the denominator:

\(\implies \dfrac{12}{2}\)

Rewrite 12 as 2 · 6:

\(\implies \dfrac{2 \cdot 6}{2}\)

Cancel the common factor 2:

\(\implies \dfrac{\diagup\!\!\!\!2 \cdot 6}{\diagup\!\!\!\!2}\)

\(\implies 6\)

Answer:

Step-by-step explanation: Three line segments can form a triangle, if the sum of any two lengths is greater than the third length. In A), 8 + 7 = 15 < 16. So, A cannot form a triangle.

Step-by-step explanation:

you have to study

Answer:

A,B and D form a triangle

Step-by-step explanation:

A - Side = 16 cm, side = 8 cm, side = 7 cm

16>8+7=15 form a triangle

B.- Side = 16 cm, side = 9 cm, side = 7 cm

16>9+7=16 form a triangle

C - Side = 17 cm, side = 12 cm, side = 7 cm

18>12+7=19 not form a triangle

D - Side = 17 cm, side = 11 cm, side = 5 cm

17>11+5=16 form traingle

Answer:

130%

increase

Step-by-step explanation:

the new quantity is 13, the old is 10

divide 13/10

in your calculator this will show 1.3

that means one whole and 30/100ths, or in percents 130%

(to convert decimal to percent just mulitply by 100)

The values of x and y that makes the expression are x = 4 and y = -5

The expression is given as

(4 + 5i)(x + yi)

The above expression is a complex expression

As a general rule, complex expressions are represented as a + bi

Where a is the real part and bi is the complex part

Also, we have

i = √-1

Using the above as a guide, we have

(4 + 5i)(x + yi)

For the above expression to be a real number, then the following must be true

(4 + 5i) must be a conjugate of (x + yi)

This means that

x + yi = 4 - 5i

By comparison, we have

x = 4 and y = -5

Hence, the values are x = 4 and y = -5

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Using it's concept, the mean absolute deviation of the data-set is of 2 sundaes.

The mean for this problem is:

(4 + 6 + 2 + 4)/4 = 4

Hence the MAD is:

(|4-4| + |6-4| + |2-4| + |4-4|)/4 = 1

Since each unit represents 2 sundaes, the mean absolute deviation is of 2 sundaes.

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Answer:(5,4) , (−9,7)

(0,1)

, (1,0)

(−5,9)

, (3,0

Step-by-step explanation:

Graph attached as solution

Answer:

4 by 3

Explanation:

Rows by columns