TRUE/FALSE. When algebraic, or numerical fractions are added or subtracted, the result is a single fraction.'

As per the unitary method, the amount of white beans are there than kidney beans are 30.

The term unitary method is known as a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.

Here we have given that in a jar containing dry beans, the ratio of white beans to kidney beans is 5:4.

And we also know that if 30 white beans were replaced with 30 kidney beans, the ratio would be 1:1.

Here we have consider that let the number of pinto beans be x and that is the number of white beans will be x + 30

In which means the total number of beans in the jar will be written as,

=> x + x + 30 = 2x + 30

Here we know that the Total ratio is calculated as,

=> 5 + 4  = 9

In order to find the number of pinto beans then it can be calculated as,

=> ratio of pinto beans / Total ratio  X Total number of beans

Which can be written as.

=>  (2x + 30) = x

When we simplify this one then we get the value of x as,

=> x = 30.

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So, the coordinates of the images S', R', T' under the translation are (11,9), (-4,-6) and T'(h+4,k-5) respectively.

a) For the point S(7,14), we are given the translation defined by (x,y) -> (x+4, y-5). This means that for any point (x,y), we add 4 to the x-coordinate and subtract 5 from the y-coordinate to find the image of that point. Applying this transformation to the point S(7,14) gives us the image point S'(7+4, 14-5) = S'(11,9). So the coordinates of the image S' is (11,9)

b) For the point R(-8,-1), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point R(-8,-1) gives us the image point R'(-8+4,-1-5) = R'(-4,-6). So the coordinates of the image R' is (-4,-6)

c) For the point T(h,k), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point T(h,k) gives us the image point T'(h+4,k-5).

Here h and k are variables and we can't say the coordinates of image point T' without specific values of h and k. But we can say the transformation of point T as T'(h+4,k-5)

So, we have found the coordinates of the images S', R', T' under the translation defined by (x,y) -> (x+4, y-5) as (11,9), (-4,-6) and T'(h+4,k-5) respectively.

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Any two angles whose sum is 146 degrees must both be less than 146 degrees. This can be supported by the Triangle Sum Theorem, which states that the sum of the measure of the interior angles of a triangle is 180 degrees.

The Triangle Sum Theorem states that the sum of the measure of the interior angles of a triangle is always 180 degrees. Therefore, if two angles add up to 146 degrees, then both of those angles must be less than 146 degrees. This is because the remaining angle must make up the difference to reach the total of 180 degrees.

Therefore, any two angles whose sum is 146 degrees must both be less than 146 degrees.

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A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

A system of linear equations is a group of equations with multiple variables. The number of solutions to the system of equations depends on how many equations and how many variables are in the system. A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

If the number of equations is greater than the number of variables, the system is said to be overdetermined and has no solutions.

If the number of equations is equal to the number of variables, the system is said to be determined and has either one or an infinite number of solutions, depending on if the equations are dependent or independent.

If the number of equations is less than the number of variables, the system is said to be underdetermined and has an infinite number of solutions.

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The numbers that can be formed using the  condition is [tex]20^n[/tex]

When a positive integer has n digits and the first digit is 2, all of the digits are prime, the probability that any two successive digits added together are prime is. Numbers from the set {1,3,5,7,9} must be used in the n odd locations, and numbers from the set {2,4,6,8} must be used in the n even spots.

We cannot include 0 in even positive integers because it is neither positive nor negative.

Order matters and repetitions are permitted.

So, here we are

possibilities are

[tex]5^n \times 4^n =20^n[/tex]

where n is the integral value

Therefore, the number of positive integers with digits and the specified restriction is [tex]20^n[/tex]

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Answer:

To find out how many plants are not flowers, we need to subtract the number of flowers from the total number of plants.

We know that 2/20 of the plants are flowers, and we can use this information to find out how many plants are flowers. To do this, we can multiply the total number of plants (260) by the fraction of plants that are flowers (2/20).

260 x (2/20) = 260 x 0.1 = 26

So there are 26 plants that are flowers.

To find the number of plants that are not flowers, we subtract the number of flower plants from the total number of plants:

260 - 26 = 234

So there are 234 plants that are not flowers.

The average price of gas per gallon this month: $3.85 per gallon.

For the stated question-

Average price of gas last month = $2.20 per gallon.

Percentage increase = 75%.

75% of 2.20 = 75*2.20 / 100

                    = 1.65

Average price of gas this month = $2.20  + $1.65 per gallon

                                                      = $3.85 per gallon

Thus, the average price of gas per gallon this month: $3.85 per gallon.

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The solution is Option C.

The equation of line is given by y = -2x + 58

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 2 , 54 )

Let the second point be Q ( 5 , 48 )

The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 54 - 48 ) / ( 2 - 5 )

On simplifying the equation , we get

Slope m = 6 / -3

Slope m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 54 = -2 ( x - 2 )

On simplifying the equation , we get

y - 54 = 2x + 4

Adding 54 on both sides of the equation , we get

y = -2x + 58

Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )

Hence , the equation of line is y = -2x + 58

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An equation that Elena can use to find the height 'h' is h = 24/b.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the area of a triangle is (1/2)×base×height.

Given, Elena is designing a logo in the shape of a triangle having an area of 12 square inches.

Therefore,

(1/2)×base×height = 12.

b×h = 12×2.

b×h = 24.

So, Elena can use the following equation to get the height 'h',

h = 24/b.

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Answer:

12 m

Step-by-step explanation:

Here's a picture to show the problem.

                                        boat

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

~~~~~~~~~~~\                                              /~~~~~~~~~~~~~~~~~~~~~~~~

                       \-----------Alexandra ---------/          surface of the water

                                          |\                              

                                          |     \

                                          |          \

                                          |               \

                                  d      |                   \      13 m

                                          |                        \

                                          |                            \

                                          |                                \

                                          | ---  rt <                         \

                          hook      -----|------------------------------    fish

                                                           5 m

There is a right angle at the hook. We have a right triangle with leg d, the distance we need to find, leg 5 m, and hypotenuse 13 m.

a² + b² = c²

5² + b² = 13²

25 + b² = 169

b² = 144

b = √144

b = 12

Answer: 12 m

the radial form is, 6 times the eight root of x to the fifth power.

Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

here, given that,

6x^5/8

now,

the radial form is,

6 times the eight root of x to the fifth power.

Hence, the radical form is, 6 times the eight root of x to the fifth power.

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In linear equation , the number of baseball cards Tom has is 434.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

We need to find the amount of cards Tom has.

The number of cards Tom has is 434.

Let the number of baseball cards Tom has be X .

Neil has 83 more baseball cards than Tom so

X + 83 is the number of baseball cards that Neil has.

The number of baseball cards Neil has is  517

So,

   x + 83 = 517

   x = 517 - 83

  x = 434

Hence, the number of baseball cards Tom has is 434.

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The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.

A polynomial is a mathematical expression that solely uses additions, subtractions, multiplications, and powers of positive integer variables. It is composed of coefficients and uncertainty. A single indeterminate x polynomial is indicated by the expression x2 4x + 7. In mathematics, a polynomial is a mathematical equation made up of variables (sometimes called indeterminates) and coefficients that can be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is a statement in mathematics involving variables and coefficients. The only operations that can be included in an expression are addition, subtraction, multiplication, and non-negative integer exponents. These formulas are known as polynomials.

given

(x - 5)(x + 2) = 0

Using the 0 product property:

Case 1

x - 5 = 0

x = 5

Case 2

x + 2= 0

x = -2

The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.

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It is plausible to assume that the die is fair because there is a 3% possibility that a loaded die might randomly yield the outcomes that we saw.

The appropriate conclusion is that there is a 3% chance that a loaded die could randomly produce the results we observed. We tested this hypothesis by rolling the die 200 times and our p-value turned out to be 0.03. This means that there is only a 3% chance that the results we observed could have been produced randomly by a loaded die, so it is reasonable to conclude that the die is fair. This is because a p-value of 0.03 is considered to be statistically significant, which indicates that the results we observed are unlikely to have been due to chance. Therefore, we can conclude that the seller's claim that the die will favor the outcome 6 is likely false.

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If something melts in your mouth and not in your hand, then it must be something that has a low melting point.

Converse,Inverse and Contrapositve

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According to the formula of area of rectangle, the length of each piece is 1.49 inches.

The formula to calculate the area of the rectangle is written as,

A = l x b

where l refers the length and b refers the breadth of the rectangle.

Here we have know that Allie is creating an art project using pieces of paper that are each 8. 06 inches long.

Here we also know that she tapes 5. 4 pieces together end-to-end.

Here the value 8.06 refers the total area of the paper and the value 5.4 refers the breadth of the paper.

Then according to the formula, the length is calculated as,

=> l = 8.06/5.4

=> 1.49

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Answer:

Step-by-step explanation:

Using the given equation, we can solve for t when s is equal to 22.

22 = -2.7t^2 + 40t + 6.5

Subtracting 6.5 from both sides, we get:

15.5 = -2.7t^2 + 40t

Adding 2.7t^2 to both sides, we get:

18.2t^2 = 15.5 + 40t

Subtracting 40t from both sides, we get:

18.2t^2 - 40t = 15.5

Dividing both sides by 18.2, we get:

t^2 - 2.2t = 0.855

Factoring, we get:

(t - 1)(t - 0.855) = 0

Setting each factor equal to 0 and solving, we get:

t = 1 and t = 0.855

Therefore, the ball will reach a height of 22ft after 1 second and 0.855 seconds.

The vertex and range of y = |x + 2| - 6 are: A. (-2, -6); -6 ≤ y < ∞.

Generally speaking, the vertex points of an absolute value function occurs when the absolute values are equal to zeros. Therefore, we would equate the x-values of this absolute value function to zero as follows;

y = |x + 2| - 6

|x + 2| = 0

x + 2 = 0

x = -2

When x = -2, the value of y for this absolute value function is given by;

y = |x + 2| - 6

y = |-2 + 2| - 6

y = 0 - 6

y = -6

Therefore, the vertex is (-2, -6).

Since |x + 2| ≥ 0, we would add -6 to both sides of the inequality in order determine the range as follows;

|x + 2| - 6 ≥ -6

y = f(x) ≥ -6

Therefore, the range of this absolute value function is defined for all real numbers that are greater than or equal to -6 i.e -6 ≤ y < ∞.

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Complete Question:

What are the vertex and range of y = |x + 2| - 6?

Carolyn made an error in her calculation. She failed to take into account the cost of labor and overhead in her equation.

Her equation only accounted for the cost of materials, not the cost of labor and overhead. The equation should have been: 12(X-3.20) + Cost of Labour and Overhead = 54. This would have given her a more accurate calculation of the profit per necklace.

In addition, Carolyn did not account for other factors such as marketing, shipping, and taxes, which could also affect the total profit. If she had taken into account these other costs, she would have been able to better calculate her profit margin on each necklace. By not accounting for these costs, Carolyn could have underestimated her profit margin, leading to an inaccurate calculation.

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The ratio of boys to girls in Ms. Cano's class is 7 to 21, there are 49 girls in the class. The total number of students in Mr. Cano's class is 196

Ratio:

In mathematics, ratios indicate the number of times one number contains another number. For example, if you have 8 oranges and 6 lemons in your fruit bowl, the ratio of oranges to lemons is 8 to 6 (that is, a ratio of 8:6, or 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to whole fruit is 8:14 (or 4:7). Ratios can be given by giving both constituent numbers written "a to b" or "a : b", or by giving only the value of their quotient a/b.

When comparing one data point (A) to another data point (B), the formula is A/B. That is, divide information A by information B. For example, if A is 5 and B is 10, the ratio is 5/10. Solve the equation. Divide data A by data B to get the ratio.

According to the Question:

Given:

The ratio of boys to girls is 7: 21,

and there are 49 boys,

Let number of boys be x and number of girls be y.

49/7 × 11 = 77 girls

Therefore,

Total number of boys and girls in the classroom is

77 + 49 = 126.

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The correct steps in the solution of the fraction are;

We know that when we talk about a fraction what we mean is just a part of a whole. There are some steps that we would need in the solution of the question and the steps have not been arranged in the proper order in the image that is attached here.

The task that we have then is to be able to arrange the steps that we need to take in the proper order and as such, we are going to have that;

Step 1 ;  2 1/2y = 5/8

Step 2 ; 5/2 y = 5/8

Step 3 ; y = 5/8 . 2/5

Step 4 ; y = 10/40 or 1/4

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The amount of money Ryan will have in his account in 6 years is $3668.71.

Compound interest is calculated using the exponential formula y = P(1+r)ⁿ. P is for "Present" or Principal value; r stands for interest rate; n stands for time (in years), and y stands for future value after the amount compounds annually

Given:

Principal Amount = $2500

Rate of interest = 6.25%

Time = 6 years

The exponential equation can be given as:

y = P(1+r)ⁿ where n is the number of years.

y = 2500(1 + 0.0625)ⁿ

The money Ryan will have in his account in 6 years can be calculated as by putting n's value as 6 years.

y = 2500(1 + 0.0625)⁶

y = $3668.71

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There are no two consecutive odd numbers that satisfy the given condition.

What are the consecutive numbers?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

consecutive numbers are defined as numbers that follow each other in the natural sequence of numbers either from largest to smallest or from smallest to largest.

Let x be the smaller odd number and y be the larger odd number. Since y is larger than x, we know that y = x + 2.

The problem states that:

2y - 2x = 21

We can substitute in the value of y:

2(x + 2) - 2x = 21

Solving for x:

2x + 4 - 2x = 21

4 = 21

This is a contradiction, so there are no two consecutive odd numbers that satisfy the given condition.

Hence, there are no two consecutive odd numbers that satisfy the given condition.

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The unit price for the apples is $1.5 per pound. The statement is true.

Now, According to the question:

How to calculate the Unit rate of the cost per pound?

8 pounds of Apple costs $12

The unit rate is

8= 12

1= x

We can write, by cross - multiply

8x = 12

x= 12/8

x= 1.5

Hence, the unit rate of the cost per pound is $1.5

And,  5 pounds of apples cost $7.50

cross multiply,

5× 12/8

60/8 = 7.50

5 pounds of apples = 7.50

Hence, The unit price for the apples is $1.5 per pound. The statement is true.

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4/3 is the valve of |MN| ^2 of a given tetrahedron  in which M AND N are the mid points of the edges AB and CD . is explained below:

on observing the diagram we can estimate that image of point D in the plane is given  by ABC is    [tex](2\sqrt{2} , 0 , -2 )[/tex]  and volume of tetrahedron ACBM is 4/3

AB=BC=CD=AD =a

hence a =[tex]2\sqrt{2}[/tex]  then MA =2 ; 2b^2 =4  ; therefore , b=[tex]\sqrt{2}[/tex]

then value of B ([tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex]    then according to the  theorem we get as

[tex]MA^{2} + MB^{2} = AB^{2}[/tex] we have condition by diagram as MA ⊥ MB similarly

MA ⊥ MC , MB ⊥ MC  hence , MA.MC =-2z =0

hence MB.MC= [tex]\sqrt{2x} +\sqrt{2y} =0[/tex] therefore we get y=-x and z=0 hence the coordinates for  C(x ,-x ,0)

and also MC^2 =2x^2=MA^2 =4 ; x=[tex]\sqrt{2}\\[/tex]  (x>0)

hence C[tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex]  hence

|MN|^2 = [tex]\frac{1}{6} |MA| . |MB| . |MC| = \frac{4}{3}[/tex]

hence the value of |MN|^2 = 4/3

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Solving the provide question, we can say that frequency distribution 70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).

In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution.

Here,

A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data.

The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9,

70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).

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The complete question is "The following data represents the age of 30 lottery winners .Given the frequency distribution for the data,

Each column (left to right) is as follows: Age, Frequency, Relative Frequency, Cumulative Relative Frequency

[20,29] 1 0.0333 0.0333

[30,39] 7 0.2333 0.2666

[40,49] 4 0.1333 0.3999

[50,59] 5 0.1667 0.5666

[60,69] 9 0.3 0.8666

[70,79] 3 0.1 0.9666

[80,89] 1 0.0333 0.9999

What is the frequency of lottery winners of age between 19 and 40?

"

If you picked a card at random, then the probability of picking a three is 1 / 4 or 25 %.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability.

The probability that you can pick a three out of the cards given is:

= Number of cards of 3 / Number of total cards

= 1 / 4

= 25 %

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The required altitude of the trapezoid ABCD is 2.5 cm.

The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.

Here, we must utilise the area of a trapezoid formula, which is

where h is the height or altitude and b1 and b2 are the two bases.

[tex]Area =\frac{ (b_{1}+b_{2})h}{2}[/tex]

Given are the values of Area = 7.5, b1 = 1, b2 = 5, and h is unknown.

Then,

7.5 = (1+5)h/2

7.5 = 3h

h = 2.5cm

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The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.

The formula to generate random numbers between 01 and 99 is (number*99/max_number)+1.

For the first number in the row, 78038, the calculation would be (78038*99/78038)+1 = 99.

For the second number in the row, 18022, the calculation would be (18022*99/78038)+1 = 25.

For the third number in the row, 84755, the calculation would be (84755*99/78038)+1 = 68.

For the fourth number in the row, 23146, the calculation would be (23146*99/78038)+1 = 17.

For the fifth number in the row, 12720, the calculation would be (12720*99/78038)+1 = 9.

For the sixth number in the row, 70910, the calculation would be (70910*99/78038)+1 = 89.

For the seventh number in the row, 49732, the calculation would be (49732*99/78038)+1 = 56.

For the eighth number in the row, 79606, the calculation would be (79606*99/78038)+1 = 97.

The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.

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Answer:

the ratio of n to m is 5 : 7

5m = 7 n

n : m = 5 : 7