Use the image to determine the direction and angle of rotation.

graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 1

270° counterclockwise rotation
180° clockwise rotation
90° counterclockwise rotation
90° clockwise rotation

There are 3/20 pink tulips

A flower garden is composed of 1/2 tulips

3/10 of this amount are the pink tulips

Therefore the number of pink tulips can be calculated as follows

= 1/2 × 3/10

= 3/20

Hence 3/20 of the tulips in the garden are pink

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Answer:

B

Step-by-step explanation:

56.54867 (the area of the bigger half circle) + 14.137165 (the area of the smaller half circle + 96 (the area of the rectangle) = 166.685835 (rounded up is 166.7 (B)).

Answer:

the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

Step-by-step explanation:

The probability of selecting a quarter or a nickel can be found by adding the probability of selecting a quarter to the probability of selecting a nickel. Since the coins are chosen randomly, the probability of selecting a coin from the jar is the number of coins of that type divided by the total number of coins in the jar.

So, the probability of selecting a quarter is:

P(quarter) = number of quarters / total number of coins

P(quarter) = 80 / (70 + 100 + 80 + 50)

P(quarter) = 0.32

Similarly, the probability of selecting a nickel is:

P(nickel) = number of nickels / total number of coins

P(nickel) = 70 / (70 + 100 + 80 + 50)

P(nickel) = 0.175

To find the probability of selecting a quarter or a nickel, we add these probabilities:

P(quarter or nickel) = P(quarter) + P(nickel)

P(quarter or nickel) = 0.32 + 0.175

P(quarter or nickel) = 0.495

Therefore, the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

Answer:

The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation

Step-by-step explanation:

It can hold 200 unit³ of popcorn.

The amount of paper used is 150 unit².

We have,

b = 8 unit

h = 5 unit

l = 10 unit

So, Volume of Triangular prism

= 1/2 x b x h x l

= 1/2 x 8 x 5 x 10

= 40 x 5

= 200 unit³

and, the amount of paper used

= 6 x 5 + 8 x 5 + 10 x 5 + 1/2 x 6 x 10

= 30 + 40 + 50 x 30

= 150 unit²

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The expressions that can be used to represent the above model are

A. The number of fourths in 1.

b. Number of fourths in three

To represent the model, we need to note the range of the figures and the number of bars in each of the specified ranges. For, 0 to 1, there are four boxes which indicate a distribution of four to 1. So, we can say that this expression is the number of fourths in 1.

Also, when we look at it on a wider level, we can say that the number of fourths in 3 is a good descriptor since there are 12 fours in the total range of 3.

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a. The distribution of X bar is  x bar - N(1022, 43.45²).

b. The distribution of x bar is x bar - N(1022, 43.45²).

c.  The probability that one randomly selected auto insurance is more than $990 is 0.1131.

d. a simple random sample of 39 auto insurance policies, the probability that the average cost is more than $990 is 0.887

a. The dispersion of X bar is ordinary with a cruel of 1022 dollars and a standard deviation of 272/√(39) dollars. In this way, X bar - N(1022, 43.45²).

b. The conveyance of x bar is additionally ordinary with the same cruel and standard deviation, so x bar - N(1022, 43.45²).

c. To discover the likelihood that one arbitrarily chosen auto protection is more than $990, able to utilize the z-score equation:

z = (990 - 1022) / 272/√(39) = -1.21. Looking up the comparing region beneath the standard typical dissemination bend, we discover a likelihood of 0.1131.

d. To discover the likelihood that the normally taken toll of a simple random test of 39 auto protections approaches is more than $990, we got to discover the z-score for this test cruel:

z = (990 - 1022) / 272/√(39) = -1.21. Employing a standard typical dispersion table, we discover that the likelihood of a z-score less than -1.21 is 0.1131. Hence, the likelihood of a test cruel more prominent than $990 is 1 - 0.1131 = 0.8869, or 0.887 (adjusted to 3 decimal places). 

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The simplified expression of log_3+log_5+log_2 32 is 5log_3(20) by properties of logarithms

Using the logarithmic identity that states log (a × b) = log a + log b

we can simplify the expression as follows:

log_3+log_5+log_2 32 = log_3(2⁵) + log_5(2⁵) + log_2(2⁵)

= 5log_3(2) + 5log_5(2) + 5log_2(2)

= 5(log_3(2) + log_5(2) + log_2(2))

using the property that log_b(a) + log_b(c) = log_b(a × c)

= 5(log_3(2 × 5× 2))

= 5(log_3(20))

Therefore, the simplified expression is 5log_3(20).

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The scale factor of the dilation is k = 5/4

Given data ,

A figure with an area of 25 square units is dilated from a figure with an area of 16 square units

Let the dilation scale factor be k

Now , Given that the original area (A) is 16 square units and the target area (B) is 25 square units, we can write the equation as:

B = k² A

k² = 25/16

Taking square roots on both sides , we get

k = 5/4

Hence , the dilation factor is 5/4

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The reason for which the graph is misleading is given as follows:

The x-axis only shows the data for one year.

The statement for this problem is given as follows:

"The yearly spending for the company has drastically decreased".

To state that the yearly spending has decreased, a comparison of the spending for multiple years must be made.

However, on the x-axis of the function, the time in years is shown for only one year, which is the reason why we can say that the graph is misleading.

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Answer:

KL=45

Step-by-step explanation:

The length of the interior diagonal of the box is .

Since, We know that;

In right triangles, the sum of the squares of the two legs a and b is equal to the square of the hypotenuse .

a² + b² = c²

Here, It is given that, a box has a base of 3 inches by 4 inches and a height of 12 inches.

We need to find the length of the interior diagonal of the box.

Now, we will find the length of the interior diagonal of the box by using the Pythagorean theorem.

So,

⇒ √3² + 4² + 12²

⇒ √9 + 16 + 144

⇒ √169

⇒ 13

Hence, 13 are the length of the interior diagonal of the box.

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Note that the probability that a student chosen at random will play an instrument besides the guitar is 29/45.

To derive the probability, that a  chosen at random will play an instrument other than guitar , we have to first find the sum total of all students who can play an instrument that is not a guitar.

From the table, we can se that this is:

3 + 10 + 5 = 18 on the 7th grade

while the 8th grade we have 3 + 6 + 2 = 11

18 + 11 = 29

So that total students in the middle school is

12 + 3  + 10 +5 + 4 + 3 + 6 + 2 =   45

hence the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form is 29/45

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The value of this expression if x = -1 and y = -5 is -5/4.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

x²y/4

(-1)² × -5/4

1 × -5/4

-5/4

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Complete Question:

find the value of this expression if x = -1 and y = -5.

x²y/4

Answer:  The domain of the function f(x) = log(-5x + 3) is the set of all real numbers x that make the argument of the logarithmic function positive.

Since the argument of the logarithmic function is -5x + 3, we must have:

-5x + 3 > 0

Solving for x, we get:

-5x > -3

x < 3/5

Therefore, the domain of the function f(x) = log(-5x + 3) is all real numbers x such that x < 3/5.

Step-by-step explanation: Hope this helps :D

Since first four points in this table have been plotted on the scatter graph, the points that shows where the last point should be plotted is C.

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) above, the coordinate points and quadrants should be identified as follows;

Point C ⇔  (130, 180) → quadrant I.

In conclusion, we can logically deduce that the each of the intervals on both the x-axis and y-axis is equal to 10 units.

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To write 8gk³-20g²k²+4g⁴f in standard form, we need to arrange the terms in decreasing order of their exponents.

So we start with the highest degree term:

4g⁴f

Then the next highest degree term:

-20g²k²

And finally, the lowest degree term:

8gk³

Putting it all together, we have:

4g⁴f - 20g²k² + 8gk³

This is the standard form of the expression.

The approximate shortest distance between the treasure chest and driftwood is 3.2 yards

The correct answer is an option (C)

From the attached figure of the coordinate plane,

the coordinates of the palm tree = (1, 2),

the coordinates of the  treasure chest = (5, 8)

and the coordinates of the driftwood = (8, 7)

We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

We need to find the distance between the treasure chest and driftwood.

Let (x₁, y₁) = (5, 8)

and (x₂, y₂) = (8, 7)

Using distance formula, the approximate shortest distance between the treasure chest and driftwood would be,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(7 - 8 )² + (8 - 5)²]

d = √[(-1)² + (3)²]

d = √[1 + 9]

d = √(10)

d = 3.1622

d ≈ 3.2 yards

This is the required distance between the treasure chest and the driftwood.

Therefore, the correct answer is an option (C)

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Find the complete question below.

A Euler Circuit in the graph is ADGFACFIECBEHDBA.

When we describe an Euler circuit, we are describing a path in a diagram known as a graph that starts and ends at the same vertex.

While you can visit a vertex a number of time, you can only visits every edge of the graph once. This means that you cannot walk the path to a vertex more than once.

For the graph in the picture, ADGFACFIECBEHDBA is the Euler circuit. You can see that vertex like A was repeated three time, E, C and F, were repeated twice.

Can this graph be called Eulerian? No, because it does not fulfill the condition.

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The three men will visit the barber shop on the same day again in 72 days.

Three men visit a barber shop on their schedule, jack visits every 18 days, bryce visits every 8 days, and jadon visits every 9 days

We have to find the how many more days before they will visit on the same day again

We want to find the least common multiple (LCM) of 18, 8, and 9.

First, we can find the prime factorization of each number:

18 = 2 × 3 × 3

8 = 2 × 2 × 2

9 = 3 × 3

Next, we can take the highest power of each prime factor that appears in any of the numbers:

2³ × 3² = 72

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Shortage of investment capital would not be considered a barrier to economic development.

All factors are considered for economic development except the following given .

Since Barriers to economic development are large population size, savings gap, large and inadequate capital accumulation, corruption, politics and poor governance, and the deficit in the foreign trade of goods and services.

Other factors lack of technological developments,  climatic and weather disturbances, a decline of trade and commerce is considered to be one of the biggest drawbacks influencing this growth.

Institutional barriers like education, skill development, innovation, and access to equal opportunities.

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Answer:y=1/4x+1/2

Step-by-step explanation:

4y=x+2

y=1/4x+1/2

Answer:

Step-by-step explanation:

A=1/2 a p                 a is apothem;  p is perimeter of base

p=22*5 =110

a you need to find by making a triangle with the radius and finding the angle of the right triangle

All external angles of any polygon =360

divide by 5 and then 2 to find triangle

=54

Use tan 54 = a/11

a=15.14

A= 1/2 *15.14 *54

408.8

The probability that exactly 3 out of 4 people chosen at random favor the new building project is 0.2904.

This problem can be solved using the binomial probability formula. Let X be the number of people who favor the new building project out of the 4 chosen at random. Then X follows a binomial distribution with parameters n = 4 and p = 0.45.

The probability of having exactly k people who favor the new building project out of 4 is given by:

P(X = k) = (4 choose k) * [tex]0.45^{k}[/tex] * [tex]0.55^{4-k}[/tex]

where (4 choose k) is the binomial coefficient.

To find the probability that exactly 3 of the 4 people favor the new building project, we substitute k = 3 in the above formula and evaluate:

P(X = 3) = (4 choose 3) * [tex]0.45^{3}[/tex] * [tex]0.55^{1}[/tex]

= 0.290384375

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The length of VX is approximately 9.4 yd.

The area of the triangle is approximately 56.4 yd².

The area of triangle = 1/2 * base * height.

To find the area of the triangle, we have to determine its height which is the length of VX.

Apply the sine ratio to find the length of VX:

sin 70 = opposite/hypotenuse

sin 70 = VX/10

10 * sin 70 = VX

VX ≈ 9.4 yd.

The area of triangle = 1/2 * base * height = 1/2 * 12 * 9.4

= 56.4 square yards

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