These two scalene triangles are similar with a scale of 2:3. What is true about these figures?

Angle of depression and elevation:The angle of depression refers to the angle above the hill.The ship is 349.8 feet away from the skyscraper's base horizontally.

You could calculate the angle of elevation, for instance, if you were standing on the ground and were looking up at a mountain's summit.

The angle between a line of sight's horizontal axis and its downward axis is known as the angle of depression.

The ship is 349.8 feet away from the skyscraper's base horizontally.

Angle of depression and elevation:The angle of depression refers to the angle above the hill.

given the aforementioned variables

The harbor is 824 feet tall.

Depression angle is 67 degrees.

SOH CAH TOA identification claims that:

Tan = opp/adj Tan = 824 Tan = 67

d = 824.8/tan67 d = 349.8 feet

Therefore, the vertical distance from the skyscraper's base to the ship is 349.8 feet.

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The measures of angles BDA and BEA  is 90 degree and the fact that AD and AE are radii of circle A tell us about BD and BE must be a tangent to the circle.

The tangents to the circle are BD and BE.

∠BDA = 90

∠BEA = 90

Radii = AD and AE

A tangent's angle with a circle's radius is always measured as a 90-degree angle.

∠BDA = 90, and since AD is a radius, BD must be a tangent to the circle.

Similar, ∠BEA = 90 suggests that BE is a tangent to the circle and that AE is a radius.

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The complete question is:

What do the measures of angles BDA and BEA and the fact that AD and AE are radii of circle A tell us about BD and BE?

The no. of subsets with at least one odd number is ²⁰C₁₀ - 1

We have the sample set to be {1, 2, 3, 4, ... 20}

Now we need to make subsets of 10 from these 20 elements.

Hence, the number of possible subsets of 10 elements will be

²⁰C₁₀

Now, there are 10 odd elements in the given sample set.

Hence the number of sets that contain at least 1 odd element

= Total no. of possible sets - no. of possible sets with no odd no.

Now since there are only 10 even numbers, there can be only one such set possible.

Hence no. of the subsets with at least one odd number is

²⁰C₁₀ - 1

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The measure of arc RT is: C. 204 degree.

arc ORT = 102° - 90°

arc = 12°

arc ROT = 180° - 2×12°

arc ROT = 180° -  24°

arc ROT = 156°

Hence:

Measure of arc RT

arc RT= 360° - 156°

arc RT = 204°

Therefore the correct option is C.

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Answer: i don't know sorry 99

Step-by-step explanation:

56+80

Answer: ∠1= 75°, ∠2= 105°, ∠3=105°, ∠4=75°, ∠6=105°, ∠7= 105°, ∠8=75°

Step-by-step explanation:

∠1 is corresponding to angle 75° which make them equal.

∠2 is supplementary to ∠1 which means they add up to 180°. Since ∠1 is 75° you would subtract 75° from 180° to get 105°.

∠3 is vertical to ∠2 which makes them equal.

∠4 is vertical to ∠1 which makes them equal.

∠6 is corresponding to ∠2 which makes them equal.

∠7 is vertical to ∠6 which makes them equal.

∠8 is vertical to 75° which makes them equal.

A) The measure of the central angle is  [tex]\frac{4}{3} \pi[/tex] .

B) The radius of the circle is 55.43 in.

A) We know,

The area of a sector is  [tex]\frac{n}{2\pi } \pi R^{2}[/tex]

where n = the degree of the central angle of the sector

          R = radius of the circle

Suppose, the measure of the central angle is x.

   [tex]\frac{x}{2\pi } .\pi .24^{2} = 384\pi[/tex]

⇒ [tex]\frac{x}{2\pi } = \frac{384\pi }{576\pi }[/tex]

⇒ [tex]x = \frac{384\pi }{576\pi } * 2\pi[/tex]

⇒ [tex]x = \frac{4}{3} \pi[/tex]

So, the measure of the central angle is  [tex]\frac{4}{3} \pi[/tex].

B) Suppose the radius of the circle is r in.

   [tex]\frac{\pi /4}{2\pi } .\pi .r^{2} =384\pi[/tex]

⇒[tex]\frac{1}{8} .\pi .r^{2} =384\pi[/tex]

⇒ [tex]r^{2} = 384\pi / \frac{1}{8} \pi[/tex]

⇒  [tex]r^{2} = 3072[/tex]

As r > 0

So, r = 55.43

Hence, The radius of the circle is 55.43 in.

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The solution to the expression when x = 3 is 26

From the question, we have the following parameters that can be used in our computation:

8x + x * 2/3

Also, we have

x = 3

substitute the known values in the above equation, so, we have the following representation

8 * 3 + 3 * 2/3

Evaluate the product

24 + 2

Evaluate the sum

26

Hence, the solution is 26

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Complete question

Given that 8x + x * 2/3, calculate the expression when x = 3

The algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3

We shall first find the lowest common multiple (LCM) of the denominators of both terms to have a single fraction and then we simplify as follows;

The denominator of 8x is 1 and 2x/3 is 3

LCM of 1 and 3 is 3

we simplify to a single fraction;

multiply the term 8x by the LCM 3

(3 × 8x + 2x)/3

multiply the term 8x by the LCM 3

(24x + 2x)/3

add the algebraic terms 24x and 2x together

26x/3

Therefore, the algebraic expression 8x + 2x/3 is simplified to a simple fraction as 26x/3.

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Answer:

Step-by-step explanation:

Answer:

20, 2.7, 7.4

Step-by-step explanation:

I completed the assingment and got it 100

The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.

Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -

(boy's height) / (boy's shadow) = (light post height) / (light post shadow)

i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)

Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.

The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)

This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)

In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

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The point that lies on the function defined by the equation is (2, 7)

From the question, we have the following parameters that can be used in our computation:

y = 2x + 3

The point in the ordered pair that lies on the graph of the equation is the solution set

Take for instance, we set x = 2

So, we have the following representation

y = 2 * 2 + 3

Evaluate the product and the sum

This gives

y = 7

When repesented as an ordered pair, we have

(2, 7)

Hence, the point is (2, 7)

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All the expressions which are equivalent to -5/2z-5/6 are given below.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

-(5/2)z - 5/6

Simplifying,

-(5/2)z - 5/6,

= -5(z/2 + 1/6) is an equivalent expression.

= -5/2 (z + 1/3) is an equivalent expression.

Therefore,  -5(z/2 + 1/6)  and -5/2 (z + 1/3) are the equivalent expressions

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Answer: 6

Step-by-step explanation:

1. 16/1 × 3/8= 48/8

2. 48/8= 6

The ratio of the number of empty tables to the total number of tables 13:21.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that 8 of the tables at Joy's Italian Restaurant are full

13 tables are empty

The total number of tables in the restaurant are 8+13=21

We have to find  ratio of the number of empty tables to the total number of tables

Empty tables = 13

Total number of tables=21

Ratio of the number of empty tables to the total number of tables 13:21

Hence, the ratio of the number of empty tables to the total number of tables 13:21.

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The system of equations is:

From the question, we have the following parameters that can be used in our computation:

Total amount invested = $110000

Using the fiollowing variable representations:

We have

a + b + c = 200000

Using the total interest earned of 7145, we have:

10.9% * a + 2.9% * b + 5% * c  = 11165

So, we have

0.109a + 0.029b + 0.05%c  = 11165

Country day invests $20000 more in bonds than in CDs.

So, we have

b = c + 20000

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The MEAN best describes the monthly rents.

The best one is Mean : 898

Now, According to the question:

The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810.

We are required to use the mean, median and mode to explain which measure of central tendency best describes the monthly rent.

The mean, median and mode (as calculated) are the measures of central tendency for the data set given.

This measures which value is closest to the center such that it can conveniently represent every other data. Observe carefully that the least value is 670 while the highest is 1550.

Also, observe that the value which is "more central" to both extremes is the mean.

The median is closer to the lowest value and much farther from the highest value.

The mode is actually at the lowest end of the data set.

However, the mean is safely between both ends. Its farther away from the least value than the median which means its moving closer to the "center" unlike the other two measures.

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Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.

What is the box method?

Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.

Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.

Here's how you can use the box method to distribute and simplify the expression:

( -5x - 2 ) ( 5x + 4 )

⇒-5x -2

⇒5x 4

⇒-25x^2 -10x + 20x - 8

⇒-25x^2 + 10x - 8

So the simplified expression is:

-25x^2 + 10x - 8.

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"No, the flowers were not put into groups first and then randomly assigned the two additives.

Now, According to the question:

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a random experiment. To avoid any ambiguity or surprise, a random experiment must be properly defined.

"Information available from the question"

The florist selects 20 flowers of different

And puts in each vase with same amount of water.

10 flowers have been assigned to receive the new additive.

The remaining 10 flowers receive the original additive.

Based on the data, this is not a randomized block design for the experiment because the flowers were not put into groups first and then randomly assigned the two additives.

Therefore,  "No, the flowers were not put into groups first and then randomly assigned the two additives.

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Answer:

Answer is in attached photo. (B)

Step-by-step explanation:

The solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:

1) Substitution Method

2) Elimination Method

Answer:

Step-by-step explanation:

Total number = 260

Ratio would be 1 : 3

So, the first part is given by

[tex]\frac{1}{4}[/tex] x 260

=[tex]\frac{260}{4}[/tex]

=65

And the second part is given by

[tex]\frac{3}{4}[/tex] x 260

=[tex]\frac{780}{4}[/tex]

=195

Hence, the first and second part are 65 and 195 respectively.

The breaking apart numbers with addition help us to solve an addition more efficient than left-to-right addition.

Addition in math is a process of combining two or more numbers.

Given that, think about what you know about breaking apart numbers with addition.

Breaking apart an addend is a mental math strategy for addition. Some students may find this method more efficient than left-to-right addition.

This strategy involves breaking up one addend in an equation into more manageable parts.

1) 32 + 46 =

Breaking the second term 46 in 40 + 6

32 + 40 + 6

= 72 + 6

= 78

2) 89 + 73 =

Breaking the second term 73 into 70 + 3

89 + 70 + 3

= 159 + 3

= 162

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The roots of the parabola are given as follows:

x = -2 and x = -4.

The quadratic function for this problem is defined as follows:

y = x² + 6x + 8.

Completing the squares, the quadratic function can be factored as follows:

y = (x + 4)(x + 2).

As:

Then the roots are obtained as follows:

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Answer:

0.01 goes in the first box

0.10 goes in the second box

Therefore, the first equation is 0.01p + 0.10d = 1.50

===========================================================

Reason:

The last part mentions "A penny is 0.01" which means $0.01 or 1 cent. The 0.01 is the coefficient of the variable p.

1 penny = $0.01

p number of pennies = 0.01p dollars

A similar situation happens with the dimes.

We need to find how much water Ella needs to make the different concentrations of syrups. The solution will be for 1.5%, we need 32.83 lbs of water.

The percentage in the concentration tells us how much in the mixture is sugar.

So for example, in the 50% syrup, we have a 50% of sugar, meaning that half of it is sugar, and we have 0.5 lbs of sugar, so we need to add the same amount of water, 0.5 lbs of water.

For the 1.5% syrup, this will be:

= (0.5 - 0.5 × 0.015) / 0.015

= 32.83 lbs

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Complete question

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case.  1.5% syrup?

Applying combination, the number of playlist is: 75,435.

A combination is a way of selecting a certain number of items from a larger set, without regard to the order of the items.

The number of possible playlists would be the number of ways to select 7 songs out of 20 without regard to order, which is commonly known as a combination.

The formula for combination is nCr, where n is the total number of items and r is the number of items being chosen at a time. So in this case, the number of possible playlists would be 20C7.

This can also be written as 20!/(7!*13!)

The answer is 75,435

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On dividing the expression [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)], the value obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression is given as - [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)]

Apply the fraction rule, (a/b)/(c/d) = a·d/b·c

= [(x²-9) × (x²-2x-15)]/[(x²-4x-5) × (x²+5x+4)]

= [(x²-9) × (x+3)]/[(x²-4x-5) × (x+1)]

Expand the expression -

= [(x²-9) × (x+3)]/(x³-3x²-9x-5)

= (x³+3x²-9x-27)/(x³-3x²-9x-5)

= 1 + [(6x²-22)/(x³-3x²-9x-5)]

Therefore, the expression obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].

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Based on a survey of 2718​ people, a research center concluded that​ 32% of Americans​ "always" make a special effort to sort and recycle​ glass, cans,​ plastic, or​ papers. Participation bias is there in this case.

The bias would have no effect on a reader's perception of the assertion because no group of persons is much more likely to respond to the poll than any other.

When comparisons are performed between groups of patients who differ in outcome determinants and the differences are connected to the result, participation bias emerges.

1. Participation bias is inherent in studies that involve participant enrollment.

2 Because selective participation might jeopardize study external validity, determining the magnitude of participation bias is critical for optimizing inference from these investigations.

Few community studies have looked into the impact of participation bias. Nonparticipants in one population-based study of myocardial infarction (MI) were older, had more comorbidity, and had a lower survival rate than participants.

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she need 240 number of participant .

Graphing cell means to picture primary impacts and connections. The numbers in the secret elements address bunch implies in a 2 x 2 x 3 plan. The negligible means for factors An and B are likewise shown. The cell implies are plotted as line diagrams and as reference charts.

Now, According to the question:

We have Dr. Green is interested in conducting a 2 x 2 x 3 within-group factorial design.

There are 12 cells in factorial, and each cell 20 participant.

Then, number of participant = 20(12) = 240 participant.

Thus, she need 240 number of participant .

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The given data is ordinal data.

This type of data is ordinal data, as the variables are collected on an ordered scale (the number of times per day the device is turned on and the number of inhalations per activation). Although the actual numerical values may not have equal distances, they can still be ordered and compared based on the magnitude of the numbers.

Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. These statistics are presented on an ordinal scale, one of the four measurement levels that S. S. Stevens described in 1946.

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The total amount of oil he would have if he pours them both in a can is 2.7 liters.

In order to determine the amount of oil he would have, add both numbers together. In order to add the numbers, both numbers have to be in the same form. One of the numbers is a decimal and the other is a fraction.

In order to convert the fraction to a decimal, divide the numerator by the denominator.

1/5 = 0.2

Total number of oil = 0.2 + 2.5 = 2.7 liters

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