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Step-by-step explanation:

To Find : size of angle x

Solution:

Area of ΔABC = (1/2) * BC * AC

=> (1/2) * BC * AC = 42

=> (1/2) * 6 * AC = 42

=> AC = 14 cm

BD = BC + CD

=> 22 = 6 + CD

=> CD = 16 cm

Tan x = AC /CD

=> Tan x = 14/16

=> Tanx = 7/8

=> x = Tan⁻¹(7/8)

=> x = 41.186°

The size of the angle is - 41. 186°

    area of triangle ABC = 1/2 * BC * AC

    or, 1/2 *BC * AC = 42

     or, 1/2 * 6 * AC = 42

     or, 3 * AC = 42

divide both sides by 3,

        AC = 14 cm

     BD = BC + CD

or, 22 = 6 + CD

or, CD = 16 cm

   tan x = [tex]\frac{AC}{CD}[/tex]

or, tan x = [tex]\frac{14}{16}[/tex]

or, tan x = [tex]\frac{7}{8}[/tex]

or , x =  41. 186°

∴ The size of the angle is - 41. 186°.

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Answer:

Below

Step-by-step explanation:

1500 = 1000 e^.03t

1.5 = e^.03t

take LN of both sides

.405465 = .03 t        t =13.5 yrs

Both of the triangles are RIGHT triangles. y X(0,13) Y(0,7) Z(0,3) (0,0) J.  the length of vertical segment XY is 6.

Generally, A part of a line that is totally vertical is referred to as a vertical line segment. This means that the two vertices that make up the segment's ends have the same x- and y-coordinates but different z-coordinates than one another.

The length of vertical segment XY can be found by subtracting the y-coordinate of point X from the y-coordinate of point Y.

In this case, the y-coordinate of point X is 13 and the y-coordinate of point Y is 7, so the length of vertical segment XY is

13 - 7 = 6.

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Answer:

The slope is -4.

Step-by-step explanation:

[tex]m = \frac{11 - 3}{0 - 2} = \frac{8}{ - 2} = - 4[/tex]

The ordered pair that is a solution to the given equation, y = | -6x + 2 |, is (1, 4)

From the question, we are to determine the ordered pair that is a solution of the given equation

The given equation is

y = | -6x + 2 |

To determine the ordered pair that is a solution to the equation, we will pick a value for x and determine the value of y for the value

y = | -6x + 2 |

Put x = 1

y = | -6(1) + 2 |

y = | -6 + 2 |

y = | -4 |

y = 4

Hence, the ordered pair is (1, 4)

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Answer: x ≥ 8

Step-by-step explanation:

      We know that our inequality must be greater than or equal to $112 because she needs at least $112 to buy the new dress. This is the first part of our inequality.

      Next, we see that she already has $40 and will earn $9 an hour babysitting, if x is the number of hours. $9 an hour can become 9x, then we will add the $40 she already has for 9x + 40 as the second part of our inequality.

      This complete inequality is:

9x + 40 ≥ 112

      Now, we can solve by isolating the variable x with inverse operations.

9x + 40 ≥ 112

9x ≥ 72

x ≥ 8

      Matilda needs to babysit at least 8 hours to afford the new dress.

Answer:

11/50

Step-by-step explanation:

=5x2+1= 11/5

=1/10×11×5

=11/50

Answer:

Step-by-step explanation:

34/5=p2

Answer:

The two equations are true for the same value because when you substitute 7 for x both of them are correct

Step-by-step explanation:

1) 3(7) - 5 = 16             3(7) = 21

27 - 5 = 16                    21 = 21

16 = 16                             True

True                                    

There are 8 players who weigh between 169 and 194 pounds.

To answer this question, we can look at the box plot to understand the distribution of weights on the football team. The box plot shows us the minimum, maximum, median, and quartiles of the team's weights. The left quartile is 169 pounds, and the right quartile is 194 pounds. This means that 25% of the team's players weigh between 169 and 194 pounds. Since the team has 36 players, 25% of 36 is 9. However, since we are looking at the number of players between 169 and 194 pounds, we need to subtract 1 since the right quartile of 194 pounds is included in the number of players. Thus, there are 8 players who weigh between 169 and 194 pounds.

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[tex]\displaystyle\\Answer:\ \frac{113}{8} =14\frac{1}{8}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\frac{113}{8}=\\\\\frac{112+1}{8}=\\\\\frac{112}{8} +\frac{1}{8} =\\\\14+\frac{1}{8} =\\\\14\frac{1}{8}[/tex]

Answer:

100n/m

Step-by-step explanation:

n = m% of x

n = mx/100

x = 100n/m

The minimum value, Q1, Median, Q3 and maximum value of the data are 10,15,21.5, 23.5 and 27 respectively. The box-and-whisker plot of data is attached

Given: 21,27,22,22,25,14,16,10

Arrange the data in ascending or descending order:

10,14,16,21,22,22,25,27

The minimum value = 10. The maximum value = 27

Find the median. The median is the value in the middle. The median values are 21 and 22. Thus:

10,14,16,21,22,22,25,27

Median (Q2) = (21+22)/2 = 21.5

Consider the values to the left of the median with one of the median numbers included (since we have two numbers in the middle): 10,14,16,21

Median = (14+16)/2 = 15

Thus, Q1 = 15

Also, consider the values to the right of the median with one of the median numbers included: 22,22,25,27

Meadian = (22+25)/2 = 23.5

Thus, Q3 = 23.5

To create a box and whiskers plot use Minimum value, Maximum value, Q1, Median(Q2) and  Q3 (Check the attached image)

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The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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Answer:

x=+/- i 6

Step-by-step explanation:

x²=+/- rad(i²*36) i²= -1

x²=+/-i rad(36) [rad = square roots]

x²=+/- i 6

The equation representing the total profit earned by Maon is Profit = 256 - 128.

Profit is calculated by the formula -

Profit = Cost price - Selling price

Cost price = 64×2

Performing multiplication to find the cost price

Cost price = $128

Selling price = 64×4

Performing multiplication to find the selling price

Selling price = $256

Keep the values in equation to find the profit

Profit = 256 - 128

Performing subtraction on Right Hand Side of the equation to find the profit

Profit = 128

Thus, the profit earned is $128.

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Chi-square independence test.

A test that evaluates how well a model matches real observed data is the chi-square (2) statistic.

A chi-square statistic can only be calculated with data that is random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a sizable enough sample.

The outcomes of a fair coin toss, for instance, satisfy these requirements.

To test hypotheses, chi-square tests are frequently employed.

Given the size of the sample and the number of variables in the relationship, the chi-square statistic examines the size of any discrepancies between the expected results and the actual results.

According to the total number of variables and samples used in the experiment, degrees of freedom are utilized in these tests to assess whether a particular null hypothesis can be rejected. as well.

According to our question-

The independence of two variables, each of which is categorized into a variety of categories or attributes, is also tested using the chi square statistic.

When the cell probabilities rely on the unknown parameters, the goodness of fit test is relevant as long as the unknown parameters are substituted by their estimates and as long as one degree of freedom is subtracted for each estimated parameter.

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10^7 ÷

your question is incomplete, please comment the full question for a more accurate answer

Answer: B

Step-by-step explanation:

Equation: S=KT

Just do S divided by T to get K and you get 7

Answer: s=7t

Step-by-step explanation:

you have to multiply every answer in the t column by 7 to get the number across in the s column

The common denominator of the fractions 2/3 and 1/6 will be 6.

The lowest common multiple is the smallest multiple which is common between any two numbers.

It means we can divide both numbers by that and that is the smallest number by which both dived.

As per the given fractions 2/3 and 1/6.

Multiply 2 in numerator and denominator in 2/3.

2/3 x 2/2 = 4/6

Now denominator is the same thus common denominator is 6.

Hence "6 will be the common denominator for the fractions 2/3 and 1/6".

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Answer:

The x-axis interval of 39 to 65 has the smallest rate of change.

Step-by-step explanation:

See the attached worksheet.  The interval of x that results in the least change in y can be visually seen by plotting the points and drawing a curve.  The curve begins to flatten as x increases.  So the smallest rate of change is between the last two points, x = 39 to 65.

This can also be calculated by finding the change in y per a change in x.  The table in the graph confirms the earlier observation.  Dx and Dy represent the "delta," or difference, D,  between the x (Dx) and y(Dy) values.  The rate of change is calculated as Dy/Dx, or the change in y divided by the change in x.  The results confirm that the 39 to 65 segment is the smallest, at 0.15.

Answer:

3 nickels and 5 pennies

Step-by-step explanation:

3 nickels = 15¢

5 pennies = 5¢

15+5=20

Answer: The y-intercept is 14

Step-by-step explanation:

The slope intercept is y=mx+b

since we already have the slope, we can write this as

y=-5x+b

substitute the points of (3,-1) into the equation and solve for b

-1=-5(3)+b

-1=-15+b

b=14

The y-intercept is 14

The y-intercept of the line is 14.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope = -5

The line passes through the point (3, -1).

The equation of the line is y = mx + c.

y = -5x + c

(3, -1) = (x, y)

-1 = -5 x 3 + c

-1 = -15 + c

-1 + 15 = c

c = 14

Thus,

The y-intercept is 14.

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Answer: y=-1/2x+4

Step-by-step explanation:

find the slope of the line given which would be-2/4 which simlifys down to 1/2 then add your b (y intercept) and that wold be 4.  

equation will be the number of shirts ordered in each size. division equation with that model the theory 45 ÷ 5 = 9

The Harbor Lighthouse gift shop ordered a shipment of 45 shirts with a special whale print. This means that we need to divide 45 by 5, in order to find out how many shirts were ordered in each size. To do this, we can use a division equation.

In this equation, 45 represents the total number of shirts and 5 represents the number of sizes. The answer to this equation will be the number of shirts ordered in each size. When we divide 45 by 5, we get 9 as our answer. Therefore, the store ordered 9 shirts in each size.

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Answer:

-38x - 14y

Step-by-step explanation:

2[x+2y - 24x - 12y + 4x + 3y]

2 [ -19x -7y]

- 38x - 14y

The answer as a mixed number in simplest form will be 1 3/4.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 1/4 - (- 1 1/2)

Now,

Since, The expression is,

⇒ 1/4 - (- 1 1/2)

Hence, Solve the expression as;

⇒ 1/4 - (- 1 1/2) = 1/4 + 3/2

                      = 1/4 + 6/4

                      = 7/4

                      = 1 3/4

Thus, The answer as a mixed number in simplest form will be 1 3/4.

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Answer: x³-4x²-2x-4

Tips:

Bring down top values, then multiply by the outside value, then put it under the next value, add, and repeat

similar triangles have a ratio and in this case the ratio is 1:2 i hope you understand