complete the ratio table below

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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Answer:

True

Step-by-step explanation:

Step 1: Find the Coordinates of the Original Triangle

(2, -2)

(6, -3)

(5, 2)

Step 2: Apply the Transformation to the Coordinates

(2-(4),-2+(3))   ->     (-2, 5)

(6-(4),-3+(3))   ->     (2, 0)

(5-(4),2+(3))    ->     (1, 5)

Step 3: Compare the points on the red triangle with the points you got

(-2, 5) = (-2, 5)

(2, 0) = (2, 0)

(1, 5) = (1, 5)

Because the coordinates are the same we can conclude that the triangle was transformed with the rule: (x,y)-> (x-4,y+3)

Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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Answer:

0.989

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.

This means that \(p = 0.53\)

6 randomly selected graduates

This means that \(n = 6\)

Probability that at least one finds a job in his or her chosen field within a year of graduating:

Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So

\(P(X = 0) + P(X \geq 1) = 1\)

We want \(P(X \geq 1)\)

So

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011\)

So

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989\)

Step-by-step explanation:

When you roll once there are 6 possible rolls

   4 or 6   would be 2 out of these 6 possible = 1/3

        1/3 * 72 rolls = 24 times expected four or six

Answer:

Number 1 could be -x.

I don't know the answer to number 2.

Number 3 is the same as 1.

Step-by-step explanation:

sorry. i probably would know the answer if i remembered.

The distance from Trinidad to Tobago via the ferry is approximately 158 kilometers, but when rounded to the nearest tens, it is approximately 160 kilometers.

The distance from Trinidad to Tobago via the ferry is approximately 158 kilometers. To determine the distance to the nearest tens, we need to round this value to the nearest multiple of 10.

To round a number to the nearest tens, we look at the digit in the ones place. If it is 0 to 4, we round down, and if it is 5 to 9, we round up.

In this case, the digit in the ones place is 8. Since 8 is closer to 10 than to 0, we round up to the nearest tens. Thus, the distance from Trinidad to Tobago can be rounded to 160 kilometers.

Rounding to the nearest tens gives us a value that is easier to work with and provides a rough estimate. It is important to note that this rounded value is not exact and may differ slightly from the actual distance. However, for practical purposes, rounding to the nearest tens is often sufficient.

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Answer:

9

Step-by-step explanation:

First, you would set up a proportion.

1.6 pounds                  1                                                                                _________   =   __________

$14.407                      x

Then, you would do 14.407 times 1, which equals 14.407. Then, you would do 14.407 divided by 1.6, which equals 9.004375 (9).

So the answer is 9

Answer:

x≥88

88

88≤x≤100

Step-by-step explanation:

83x3=249

249-73-88=88

x≥88

88

88≤x≤100

Answer:

Craig's collection increased by 20%.

Step-by-step explanation:

Original amount: 10

New amount: 12

To find the percent increase, we first need to find how much Craig's record collection increased by. To do this, subtract the old amount from the new amount:

12 - 10 = 2

The amount his collection increased by is 2. To find the per cent increase, divide 2 by the original amount of records:

\(\frac{2}{10}=\frac{1}{5}= 0.20\)

Convert the decimal into a percentage:

0.20 * 100 = 20%

The percent increase of Craig's record collection is 20%.

The area of the square and the circle is computed below based on the information.

Radius = 3

Area of circle = πr² = π × 3² = 9π

Area of square = 4r² = 4 × 3² = 36

Length of square = ✓36 = 6

Ratio = 1/4π

Radius = 4

Area of circle = πr² = π × 4² = 16π

Area of square = 4r² = 4 × 4² = 64

Length of square = ✓64 = 8

Ratio = 1/4π

Radius = 2r

Area of circle = πr² = π × 2r² = 2πr²

Area of square = 4r² = 4 × 2r² = 8r²

Length of square = ✓8r² = 2✓2r

Ratio = 1/4π

The relationship between the area of the circle and the square is that the area of the square is 4 times that of the circle.

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Answer:

With speed of 18 feet per second the distance between the twins change.

Step-by-step explanation:

v1 is 10

v2 is -8

So, the difference is (10)-(-8)

which is 18.

Answer:

The distance of 2 feet with a speed of 10 feet per second.

Answer:

Answer: D

Step-by-step explanation:

I took the test and got it right i promise

A is the point of representation of (–3).

A number system is defined as a system of writing to express numbers.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

Tang created a number line for his class to use.

A number line has points negative 4, A, B, blank, 0, blank, C, D, 4.

-4, A, B, blank, 0, blank, C, D, 4.

We know that number line has integers which has positive and negative numbers.

To the left side of zero we have negative numbers and to the right side of zero the values are positive.

The values will be -4,-3,-2,-1,0,1,2,3,4

The value to the right side of -4 is -3.

In the Tang number line the value at A is -3.

Hence, A is the point of representation of (–3).

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A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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The number of possibilities for 8 of 37 servers to fail is 38608020

From the question, we have

Total number of servers, n = 37

Numbers to servers that fail, r = 8

The number of ways for 8 serves to fail is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 37 and r = 8

Substitute the known values in the above equation

Total = ³⁷C₈

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 37!/29!8!

Evaluate

Total = 38608020

Hence, the number of ways is 38608020

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Answer:

a. parameter

b. descriptive statistics

Step-by-step explanation:

The values of the population charactersitics are summarized by certain numerical descriptive measures called parameters.

The observations composing a sample are used to calculate a corresponding numerical descriptive measure called a statistic.

a. The percent of Americans is of a population and therefore it is a parameter not a statistics.

b. Descriptive statistics deals with the collection, summarization and display of data.

Inferential statistics deals with conclusions drawn based on a sample.

This is descriptive statistics because it is displaying of data collected from a population of America.

Answer:

52

Step-by-step explanation:

find the area of each individual piece

top and bottom dimensions are 4 X 3- so each one is 12 inches squared

the left and right side dimensions are 4 X 2- each one is 8

the front and back dimensions are 3 X 2 each one is 6

Surface area- add all together

12+12+8+8+6+6= 52 in squared

Answer:

Scalene

Step-by-step explanation:

It cannot be a equilateral triangle because it would have to have 3 equal sides and angles.

Isosceles triangles would need to have two equal angles and sides.

It therefore has to be a scalene triangle because it has 3 different sides and 3 different angles.

An equilateral triangle must have:

This triangle has:

Since this triangle does not have angles measuring 60° each, this is not an equilateral triangle.

An isosceles triangle must have:

This triangle has:

Since this triangle does not have two angles that are equivalent, this is not an isosceles triangle.

A scalene triangle must have:

This triangle has:

Since this triangle has all three angles that are different from each other, this is a scalene triangle.

In conclusion, this triangle is classified as a scalene triangle.

Answer:

Step-by-step explanation:

H(n)=91x(-1/7) n-1

do not know

Hope it helps the answer is the 2nd one have a great day

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:

600

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

-12°F +  3 =-9

1/2 * 6 = 3

Answer:

x = 30° ; y = 45°

Step-by-step explanation:

Angle subtended by the diameter on any point of the circle is 90°. So,angleRSP = 90°

angleRST = 120° (given)

But,

angleRST = angleRSP + anglePST

\( = > 90 + x = 120\)

\( = > x = 120 - 90 = 30\)

In triangle PQR , PQ = RQ (given)

Hence , it is an isosceles triangle. As it is an isosceles triangle , the base angles are equal.

=> anglePRQ = angleRPQ = y°

anglePQR = 90° (Angle subtended by diameter on any point of circle is 90°)

According to Angle Sum Property of Triangle,

anglePRQ + angleRPQ = anglePQR

\( = > 90 + y + y = 180\)

\( = > 2y = 180 - 90 = 90\)

\( = > y = \frac{90}{2} = 45\)

The formula for calculating the perimeter of a rectangle is

perimeter = 2(length + width)

Perimeter of the given rectangle = 2(15 + 5) = 40

Area = 5 x 15 = 75

Looking at the given options,

A) Perimeter = 2(11 + 7) = 36

Area = 11 x 7 = 77

B) Perimeter = 2(11 + 9) = 40

Area = 11 x 9 = 99

Thus, the correct option is B

a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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ANSWER

EXPLANATION

The symbols we use for inequalities are <, >, ≤ and ≥. The last two are the combination of the first two and the equal symbol.

Inequalities are usually read from left to right, so the meaning of the symbols are

• a ,<, b → a is ,less than, b

• a ,>, b → a is ,greater than, b

• a ,≤, b → a is ,less than or equal to, b

• a ,≥, b → a is ,greater than or equal to, b

Hence, in these three inequalities we have:

• h ,>, 50 → h is ,greater than, 50

• h ,≤, 20 → h is ,less than or equal to, 20

• 30 ,≥, h → 30 is ,greater than or equal to, h

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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