Given that a = 8 cm and b = 21 cm, work out A rounded to 1 DP.

The solution of the system of equations:

-2x - 10y = -2

-4y = x

is the point (-4, 1).

Here we want to solve the system of equations below:

-2x - 10y = -2

-4y = x

By the substitution method, to do so, we need to isolate one of the variables in one of the equations and then replace that in the other equation.

We can see that x = -4y is already isolated on the second equation, then we can replace this on the first one to get:

-2*(-4y) - 10y = -2

We can solve this for y.

8y - 10y = -2

-2y = -2

y = -2/-2 = 1

And thus, the value of x is:

x = -4y

x = -4*1 = -4

The solution of the system is (-4, 1).

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Answer:  1.25 or 1, 1/4

Answer:

Okay so the answer would be 8 cups

Step-by-step explanation:

the reason this is is because if you combine the cups its 2 2/3 so then all you have to do is multiply it by 3 and then your answer is 8 cups of sugar

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 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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The probability of choosing a perfect cube is [tex]\frac{7}{502}[/tex] .

According to the question,

Suppose a number is chosen at random from the set {0,1,2,3,...,501}.

Cube of 1=1

Cube of 2=8

Cube of 3=27

Cube of 4=64

Cube of 5=125

Cube of 6 = 216

Cube of 7 = 343

Cube of 8 = 512

So in a set of members {0,1,2,3,... 501}, only 7 numbers are a cube of a natural number: 1,8,27,64,125,216,343.

The probability of selecting cubes in a set of members {0,1,2,3,... 501} is

= [tex]\frac{7}{502}[/tex]

So, the probability is [tex]\frac{7}{502}[/tex] .

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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 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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Answer:

y=3x+5

Step-by-step explanation:

an equation is always

y= slope*x + intercept so y=3x+5

The translation rule that defines a translation 5 units right and 2 units up is given as follows:

(x,y) -> (x + 5, y + 2).

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

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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 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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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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The set of natural numbers between 11 and 155 is {12, 13, 14, 15, ..., 154}.

A natural number is a positive integer, also known as a counting number. The set of natural numbers is represented by the symbol {1, 2, 3, 4, ...}.

The set of natural numbers between 11 and 155 includes all the natural numbers that are greater than or equal to 12 and less than or equal to 154.

This set is represented by {12, 13, 14, 15, ..., 154}. This set is infinite, meaning it contains an infinite number of elements. The dots indicate that the set goes on infinitely in both directions, but in this case, we are only concerned with the numbers between 11 and 155.

It is important to note that the answer "A" is incorrect because it only contains 2 elements, while the correct answer B is infinite set of numbers between 11 and 155 inclusive.

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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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Adam has gathered 232.32 g of trace elements, which are contained in a cylindrical container with a radius of 8.4 cm and a height of 10.8 cm.

Radius of the cylinder 8.4 cm

Height of the cylinder = 10.8 cm

Volume of the cylinder = π r² h

When we change the values in the formula, we obtain:

V = π (8.4 cm)² (10.8 cm)

V = 22 / 7 (70.56 cm²) ( 10.8 cm)

V = 2395.008 cm³

Presence of particle = 0.097 g for every cm³

The element's trace for 2395.008 cm3 will be:

= 2395.008 × 0.097 g

= 232.315776 g

As a result, Adam has gathered 232.32 g of trace elements in the cylindrical container with a radius of 8.8 cm and a height of 15.9 cm.

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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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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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Answer: i don't know sorry 99

Step-by-step explanation:

56+80

To find the value of FG, FG is 11.

When there exist a triangle which has two of its sides to be equal in length, then it can be referred to as an isosceles triangle. Such that its two angles opposite the equal sides have equal measure.

Considering the given question, to find the value of FG;

since it has been given that <F ≅ <H, then;

GH ≅ FG  (properties of sides of an isosceles triangle)

Such that;

GH = 11, then

GH ≅ FG = 11

Thus the value of FG is 11.

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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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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?

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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The length of the segment MP is 38 units

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

The triangle

On the triangle, we have

9x - 34 = 3x + 14

Evaluate the like terms

6x = 48

Divide by 6

x = 8

Given that

MP = 9x - 34

We have

MP = 9 * 8 - 34

Evaluate

MP = 38

Hence, the length of MP is 38 units

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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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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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Answer:

D) two solutions

Step-by-step explanation:

because the first one is: x = 5y + 4

and the second one is: -2x+10y=8

and the equals in the first one is just how to get the value of x and it doesn't count as a third solution

"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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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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The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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