if a meal costs $74.30, the tax is 7%, and you want to leave a 13% pre-taxed tip, how much do you pay in total?

Given the information, the triangle congruence prove is explained below.

If the corresponding sides or measure of angles of two or more triangles have common properties, then the triangles are said to be congruent. Such that on comparing their sides and internal angles, some have equal values.

With the given information in the question, the prove is explained below:

               STATEMENTS                         REASONS

1. AB ≅ CD                                             Given

2. <ABD ≅<CDB                                    Given

3. AD ≅ BC                                            Equal sides of a parallelogram

4. <ADB ≅ <CBD                                   Alternate angle theorem

5. <A ≅ <C                                             Opposite property of a parallelogram

Therefore, it can be deduced that;

ΔABD ≅ ΔCDB

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The solution for linear equations given will be x=-1 and y=2 using substitution method.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now

Given 4x+3y=2 -->1

x-2y=-5 --->2

Using substitution method, In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation.

From 2,  x=2y-5

Put x=2y-5 in 1

4(2y-5)+3y=2

11y-20=2

y=22/11

y=2

Hence,

           x=2*2-5

             x= -1

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An equation to determine the radius of the hula hoop is diameter/2 and the  radius is 0.35.

The term called equation in math is known as a mathematical statement that is made up of two expressions connected by an equal sign.

Here we know that the Sandra measures the diameter of a hula hoop as 0. 7 m.

Here we need to write and solve an equation to determine the radius of the hula hoop.

As we all know that radius is defined as the distance from the center of the circle to any point on it's circumference.

And the term diameter is defined as a straight line passing through the center of a figure or body.

So, the diameter is calculated by using the formula,

=> d = 2r where r refers the radius.

Then the equation to calculate the radius is written as,

=> r = d/2

then the equivalent radius value is,

=> r = 0.7/2 = 0.35

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The difference between their heights in feet and inches is 6'6.3"

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

Robert Wadlow was 8’11” tall.

Pingping was 2’4.7" tall

The difference in their heights can be calculated by subtracting the smaller height from the larger

So, we have

Difference = 8’11” - 2’4.7"

Evaluate the difference

Difference = 6'6.3"

Hence, the difference is 6'6.3"

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The graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24 .

A linear relationship is depicted by a trend line. Y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept, is the equation for a linear relationship.

a graph line indicating the general path that a collection of points appears to take.

When plotting predictions, trendlines, also referred to as lines of best fit or regression lines, are frequently used to graphically represent trends in data series. Typically, a trendline is a line or curve that crosses or links two or more points in a series to indicate a trend.

From the graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24.

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Answer: -1.9d + 5.4h - 13

Step-by-step explanation:

There must be some reason why Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12: I bought just enough packets of each to have the same number of each therefore the number of items which were on the receipt is eleven (11).

This is referred to as an operation that represents the basic idea of repeated addition of the same number and will be used to get the same number of each in this scenario.

Since Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12, to get the same number of each will be to look for values which when multiplied will give the same number which are 6 and 5 respectively to give equal number of 60 each. therefore the number of items on the receipt will be 6+5 = 11.

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Answer:

Step-by-step explanation:=2/11+10/5

                                            =10/55+110/55

                                            =120/55

                                            =24/11

The cor() returns the correlation between two variables.

Correlation shows us how strong the relationship is between two variables.

Hence, option (c) is the correct choice.

Correlation quantifies the intensity of a link between two variables and is symmetrical, meaning that the correlation between A and B is the same as the correlation between B and A.

Correlation is a statistical term that describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). It's a common way of explaining simple interactions without stating a cause and effect relationship.

In R, the cor() function is used to calculate the correlation coefficient between two vectors. Correlations may be generated using the cor() function, while covariances can be generated using the cov() function. The type of correlation is specified.

There are three options: Pearson, Spearman, and Kendall.

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The complete questions should be like:

A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?

A sd()

B mean()

C cor()

D bias()

The coordinates of vertices after dilation by scale factor of 1.5 with center of dilation is D'(3,-3), E'(6,-3) and  F'(1.5,-6).

A dilation is just a transformation which enlarges or contracts the size of a figure. This means that the preimage and image are similar and are scaled up or down using a factor.

The vertices of the triangle are D(2,-2), E(4,-2), F(1,-4).

The origin-centered dilation with a scale factor of k is defined as,

(x,y) → (kx,ky)

As a result, dilation with a scale factor of 1.5 centered at the origin is defined as,

(x,y) → (1.5x,1.5y)

The image's vertices are

D(2,-2) → D'(3,-3)

E(4,-2) → E'(6,-3)

F(1,-4) → F'(1.5,-6)

Therefore the coordinates of vertices after the dilation by the given scale factor 1.5 is D'(3,-3), E'(6,-3) and  F'(1.5,-6).

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The scale factors of the shapes are 1.25, 1.25. 5 and 2, respectively

To do this, we divide the side length of the larger shape with the corresponding side of the small shape

using the above as a guide, we have the following scale factors calculations

figure 7 = 15/12 = 1.25

figure 8 = 25/20 = 1.25

figure 9 = 40/8 = 5

figure 10 = 10/5 = 2

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Answer:

60

Step-by-step explanation:

You're not slow.

So given was the formula for perimeter

12x + 1/2 - 4x - 8.5 + 2x + 8

They want you to find perimeter is x = 6, so this is a matter of plug and play. so everywhere you see an x, you'll replace it with the number 6

And we will start simplifying what we can

P = 12(6) + 1/2 - 4(6) - 8.5 + 2(6) + 8

P = 72 + 0.5 - 24 - 8.5 + 12 + 8

P = 72 - 24 - 8 + 12 + 8

P = 72 - 12

P = 60

The value of X are 5/6,1/5

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

x ÷ 5/6 = 1....1

x ÷ 2 = 1/10....2

Equation.1

(x/5)*6=1

6x/5=1

x=5/6

Equation.2

x/2=1/10

x=2/10

x=1/5

Therefore, the value of x in equations will be 5/6 and 1/5

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To go from slope intercept form of line to standard form Ax + By + C = 0, collect all terms on the left side of the equation and multiply by the denominator B.

We know that the standard form of equation of line is Ax + By + C = 0. And the slope intercept form of line is y = mx +b, where m is the slope of the line, and b is the y-intercept i.e., the value of y when x = 0.

Converting from slope intercept form to standard form:

⇒ y = mx + b

⇒ y - mx = (mx - mx) + b           .........(subtract mx from each side)

⇒ y - mx = b

⇒ y - mx - b = b -b                    .........(subtract b from each side)

⇒ y - mx - b = 0

⇒ - mx + y - b = 0

Above equation is of the form Ax + By + C = 0

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In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class.

Cumulative frequency is a running total of the frequencies of a data set. It is used to keep track of how many observations fall within a certain range of values. It is the sum of the frequencies of all the classes up to a certain point.

The second class is 1150-1219 which means it includes the price of refrigerators that fall within the range of $1150 and $1219. To find the cumulative frequency of the second class, you would need to count the number of prices in the data set that fall within that range and add it to the cumulative frequency of the previous class.

In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class. Since the cumulative frequency of the first class is not provided, we cannot calculate the cumulative frequency of the second class without more information.

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the sum is 1) 5/3, 2) 5/6 , 3) 7/10 and the difference is 1) 1/6 , 2)2/15, 3) 1/30. When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator.

1. 1/3+2/3 = 5/3

2. 1/2 + 1/3 = 5/6

3. 2/5+1/2 = 7/10

1. 1/2-1/3 = 1/6

2. 4/5-2/3 = 2/15

3. 4/15-1/10 = 1/30

When adding or subtracting fractions with unlike denominators, the first step is to convert the fractions so that they have a common denominator. To do this, you can use the lowest common denominator, which is the least common multiple of the denominators. For example, in the first problem, the least common multiple of 3 and 2 is 6, so you can convert the fractions to 2/6 and 4/6, or 1/3 and 2/3. Then, you can add or subtract the fractions as normal. For example, 1/3+2/3 would equal 3/3 or 1.

For subtracting fractions with unlike denominators, the same process is used. For example, in the second problem, the least common multiple of 5 and 3 is 15, so you can convert the fractions to 4/15 and 2/15. Then, you can subtract the fractions as normal. For example, 4/15-2/15 would equal 2/15.

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Amanda's explanation is not correct. The growth factor of an exponential function is the constant value that the function is multiplied by for each expansion in the information variable.  

It is not determined by dividing one value in the table by the previous value.

To find the growth factor of an exponential function, one ought to take the proportion of any two consecutive f(x) values and distinguish the normal proportion. The growth factor is equivalent to this normal proportion.

For instance, assuming the function is [tex]f(x) = 2^x[/tex], and the table of values is:

x f(x)

0 1

1 2

2 4

3 8

The growth factor can be tracked down by taking the proportion of f(x) values for consecutive x:

f(1)/f(0) = 2/1 = 2

f(2)/f(1) = 4/2 = 2

f(3)/f(2) = 8/4 = 2

For this situation, the growth factor is 2, meaning that the function is multiplied by 2 for each increase in x.

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Answer:

0.25 cup of rice; 13 cup of water

Step-by-step explanation:

2 cup of water: 1 cup of rice = 2:1 ratio

Answer:

C. gaining confidence

Oliver runs a mile in 6 minutes. He runs 2 miles North and 3 miles east, so the total distance he ran is 2 + 3 = 5 miles.

Since he ran the same distance back to his house, the total distance he ran is 52 = 10 miles.

Since he runs a mile in 6 minutes, the total time of Oliver's run was 106 = 60 minutes.

Therefore, Oliver's total run time is 60 minutes.

Step-by-step explanation:

I am not sure what you mean. you don't round the intermediate numbers and results. only the final result.

you keep the irrational terms (like square root) like variable terms as they are and apply operations on them without actually expressing them as numbers.

only at the very last moment (when the final result is calculated) would you express them as actual number. and then you round the final result.

so, this is solved via Pythagoras :

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

in our case we have

BP² = BN² + NP² = 7² + sqrt(95)² = 49 + 95 = 144

you see ?

no need ever to bring the actual result of sqrt(95) into the picture. just keep it at sqrt(95) and do with it, what you would do with any actual number.

BP² = 144

BP = sqrt(144) = 12

so, we never had to deal with the actual irrational number.

we know how it is created, so we keep using that term to represent it.

The correct statement is parameter because the value is a numerical measurement describing a characteristic of a population.

A parameter is a numeric value that describes a population feature in probability and statistics. It is a fixed value that is typically unknown and used to define or describe a probability distribution. The population's mean, variance, and standard deviation are a few examples of parameters.

Typically, these parameters are calculated using statistical techniques like maximum likelihood estimation from a sample of data. One can learn something about the entire population from a parameter. In the case of a given question, this implies that after asking everyone in that group, one will know something. All 1506 seniors at college were included in the survey and it was discovered that 65% of them own a television.

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Answer:

Step-by-step explanation:

6. XZY

7. YX

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{9}{8}}x-9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{9}{8}} ~\hfill \stackrel{reciprocal}{\cfrac{8}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{8}{9} }}[/tex]

so we're really looking for the equation of a line whose slope is -8/9 and it passes through (-2 , 2)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{8}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{8}{9}}(x-\stackrel{x_1}{(-2)}) \implies y -2= -\cfrac{8}{9} (x +2) \\\\\\ y-2=-\cfrac{8}{9}x-\cfrac{16}{9}\implies y=-\cfrac{8}{9}x-\cfrac{16}{9}+2\implies {\Large \begin{array}{llll} y=-\cfrac{8}{9}x+\cfrac{2}{9} \end{array}}[/tex]

The triangle created by the coordinate axes and the line with slope 3 has a 6 square unit area.

Given that the height (distance of the line from the origin) is 2 units, the area of the triangle is equal to

= (1/2)×(hypotenuse)×(height),

=6.66 square units.

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

n = a/b = change in b/change in a

where "n" represents a line's slope.

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The triangle formed by the coordinate axes and the line with slope 3 has a surface area of 4.44 square units.

As per data, we have,

Given a height of 2 units (distance of the line from the origin), the area of the triangle is equal to = (1/2)(hypotenuse) (height)

The solution is the same whether the line passes by the origin on the right or the left.

The sloping line will be the hypotenuse of a triangle whose other two sides are x or y-axis segments terminating at the origin.

The triangle's angles are 71.56 degrees (arctan3), 90 degrees, and 18.44 degrees.

The value of the length of the side opposite the tiny angle will be = 2/sin18.44 = 6.32 units

The hypotenuse length is 6.32/cos18.44 = 6.66.

The area of the triangle is calculated as (1/2)*(hypotenuse)*(height) = 4.44 square units.

The formula for the change in the y-coordinate with respect to the change in x-coordinate is: n = a/b = change in b/change in a

where "n" represents a line's slope.

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Some steps you might take after coming to a solution include all of the following:

A. Create a logical name for the variable.

E. Present your answer with units.

In Computer technology and Mathematics, a problem solving process can be defined as a systematic approach that is used typically for identifying and determining the optimal and effective solution to a particular problem.

Generally speaking, you must ensure that a logical name for the given variable is created after developing a solution to any mathematical or scientific problem.

In conclusion, the final answer (solution) must be presented with the correct and appropriate unit of measurement.

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Answer: There are 114 red marbles contained in the bag containing 120 marbles.

Step-by-step explanation:

To find the amount of red marbles in the bag:

From the question, we can presume that for every 19 marbles in a bag, there exist a single black marble. This is the same case for the total number of marbles (both red and black) in each set is 20 marbles

Set of marbles: 120/20

Red marbles:

19r = 19 x 6

19r  = 114 red marbles.

I hope this helps!

If one column of dots on the dot plot is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week.

A dot plot is a simple graphical representation of data where each data point is represented by a dot or mark above a number line. In this context, the dot plot shows the number of pizzas sold at a local restaurant each day for one week. The height of the column of dots represents the number of pizzas sold on that particular day.

If one column of dots is much taller than the others, it means that on that particular day, the restaurant sold significantly more pizzas than on the other days of the week. This could be due to a variety of reasons such as a special promotion, a holiday, or just a generally busy day.

Understanding which days are the busiest for the restaurant can help the management make decisions such as staffing levels, inventory management, and marketing strategies. For example, if a particular day of the week is consistently the busiest, the restaurant may want to offer a special promotion or discount on that day to attract more customers.

In terms of percents, if for example, the restaurant sold 100 pizzas on the day with the tallest column of dots, and the next highest day sold 60 pizzas, the day with 100 pizzas would be 166.6% higher than the day with 60 pizzas. It indicates the significance of the difference between the two days in terms of sales.

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