help plssss explainnn!!

The scale of the map = 682.5.

We kept a safe distance and followed them. She perceives a separation between her and her brother that wasn't there before. Although they were previously close friends, there was now a great deal of gap between them.

We must calculate the ratio of the distance shown on the map to the real distance between the cities in order to ascertain the scale of the map.

We are aware that there are 210 miles separating the two cities. Let x represent the precise location of this distance on the map. From that, we may establish the ratio:

Actual distance / Map Distance = 210 / x

The distance on the map is indicated as 3 1/4 inches, which is also known as 13/4 inches. When we enter this into the percentage, we obtain:

Actual distance divided by (13/4) = 210 / x

We can cross-multiply and simplify to find x's value:

Actual distance: 682.5 = x * 210 x = 3.25 when 210 * (13/4) Equals x.

Consequently, 3.25 inches on the map represent the actual distance between the cities. We can write: To determine the map's scale:

Actual distance divided by 1 inch on the chart equals 210 miles.

When we replace the values we discovered earlier, we obtain:

1 / 210 = 3.25 / scale

If we solve for the scale, we obtain:

scale = 682.5.

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Answer:

Step-by-step explanation:

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Residual  for the 5th observation if =$500 and =$475 is  -$166.25 The consumption function C = 300 + 0.75i represents the relationship between consumption and income in a simple economy with no taxes. In this function, C is the dependent variable, while i is the independent variable.

To find the residual for the 5th observation, we need to first calculate the predicted value of consumption (C1 ) for the given value of income (i). We can do this by plugging the value of i into the consumption function and solving for C1 :

C1 = 300 + 0.75i

For the first scenario where i = $500, the predicted value of consumption is:

C 1= 300 + 0.75($500) = $675

To calculate the residual, we need to subtract the predicted value of consumption from the actual value of consumption (C):

Residual = C - C1+

For the 5th observation where C = $500, the residual would be:

Residual = $500 - $675 = -$175

This means that the actual value of consumption is $175 less than the predicted value based on the consumption function.

Similarly, for the second scenario where i = $475, the predicted value of consumption would be:

C1 = 300 + 0.75($475) = $641.25

And the residual would be:

Residual = $475 - $641.25 = -$166.25  

In both cases, the residuals are negative, indicating that actual consumption is less than predicted consumption. This could be due to factors such as unexpected changes in consumer behavior, fluctuations in the economy, or measurement errors in the data.

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The equation for a consumption function in a simple​ economy, where there are no​ taxes, is given by C​ = 300 ​+ 0.75​i,  What is the residual for the 5th observation if =$500 and =$475?c denotes consumption and i denotes income.

So,

120% is the same as 1.2 or 6/5.  80% is the same as 0.8 or 4/5.

We are given the value of a, which is 12.

6/5 of a, or 1.2 times a, is equal to 4/5 of b, or 4/5 times b.

[tex]\dfrac{6}{5} (12)=\dfrac{4}{5} b[/tex]

Simplify.

[tex]\dfrac{72}{5} =\dfrac{4}{5} b[/tex]

Multiply both sides by 5/4.

[tex]\dfrac{72}{4} \ \text{or} \ 18=b[/tex]

Therefore, the sum of a and b is 12 + 18 = 30.

The statement "car:toyota" correctly describes a subclass (Toyota) of the superclass (car). Similarly, "ducks:pond" correctly describes a subclass (ducks) of the superclass (pond). So, option A) and B) are correct.

Superclasses and subclasses are used in object-oriented programming to create a hierarchical relationship between classes. In this hierarchy, a subclass is a specialized version of a superclass.

The statement "car:toyota" and  "ducks:pond" correctly describes a subclass (Toyota, ducks) of the superclass (car, pond). However, "toes:feet" and "rock:stone" do not correctly describe a subclass-superclass relationship. Rather, they describe a part-whole relationship. Toes are part of feet and rock is a type of stone.

It is important to note that a subclass can inherit traits from its superclass, but it may also have its own unique traits and restrictions. For example, a Toyota car may have some traits inherited from the car superclass, but it may also have unique features that set it apart from other car subclasses.  So, correct answer are option A) and B).

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____The given question is incomplete, the complete question is given below:

check all statements, that correctly describe traits and restrictions of superclasses and subclasses.

car:toyota

ducks:pond

toes:feet

rock:stone

(a) Mean: 207.7

(b) Median: 207

(c) Mode: None

(d) Range: 198

(e) Variance: 3705.5

(f) Standard deviation: 60.72

(g) Coefficient of variation: 29.34

Answer:

x=6

Step-by-step explanation:

Because the angles will be equal we set the equations to be equal to each other

4x+19=6x+7

12=2x

x=6

In linear equation, 65.625% of the pupils travel by bus.

What is  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. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A) 1800 * 0.55 * 0.3 = 297 Girls.

B)  1800 * 0.45 * 0.7 = 567 boys

C)  Girl

      297/864 * 100%  = 34.375%

  boy -

       567 ÷ (297 + 567 ) * 100%  = 65.625%

         864 = 297 + 567

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(a) The natural coefficient of variation for one patient is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(b) If the admission times of patients are independent, the mean and variance of admitting a group of 50 emergency patients can be calculated as follows:

mean = n x mean time = 50 x 5 = 250 minutes

variance = n x variance of individual patient / sample size = 50 x (3)^2 / 50 = 9

The coefficient of variation for a group of 50 emergency patients is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(c) The effective mean and coefficient of variation of the admission time for a group of 50 trauma patients can be calculated using the following formula:

te = n x mean time / (1 - p1 x p2)

where p1 is the probability of machine failure and p2 is the probability of repair completion. Assuming the machine can fail at any time, p1 can be calculated as 1 / (mean time between failures / mean admission time) = 1 / (80 x 60 / 5) = 0.001042. Assuming the repair time is also exponentially distributed, p2 can be calculated as 1 / mean repair time = 1 / 4 = 0.25. Therefore, te = 50 x 5 / (1 - 0.001042 x 0.25) = 250.14 minutes. The variance of the admission time can be calculated using the formula:

σe^2 = n x variance of individual patient / (1 - p1 x p2)^2 = 50 x (3)^2 / (1 - 0.001042 x 0.25)^2 = 10.81. The coefficient of variation for a group of 50 trauma patients is the ratio of the standard deviation to the mean, expressed as a percentage:

Ce = (standard deviation / mean) x 100% = (sqrt(10.81) / 250.14) x 100% = 2.60%.

(d) The variability class of the squared coefficients of variation can be determined as follows:

C0² (Part a): (0.6)^2 = 0.36 (low variability)

C0² (Part b): (0.6)^2 = 0.36 (low variability)

Ce² (Part c): (0.026)^2 = 0.000676 (low variability)

(e) The manager of the center can improve the inflated effective admission time in Part c by implementing preventive maintenance measures to reduce the probability of machine failure, such as regular inspection and cleaning of the X-Ray machine, and by improving the repair process to reduce the mean repair time, such as hiring more skilled technicians or improving the repair procedures.

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The required value of TV is 2 units.

A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.

We have given that;

TW = y²

WV = 2y − 1

We know that in parallelogram

TW = WV

y² = 2y − 1

y² - 2y + 1 = 0

y² - y - y + 1 =0

y(y - 1)-1(y - 1) = 0

(y - 1)(y - 1) = 0

(y - 1)² = 0

y - 1 = 0

y = 1

So;

TV = TW + WV

TV = y² + 2y − 1

TV = 1² + 2(1) - 1

TV = 1 + 2 - 1

TV = 2 units

Thus, required value of TV is 2 units.

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Answer:

60 degrees

Step-by-step explanation:

cos(x)=1/2

cos(x)=0.5

(x)=[tex]cos^-1[/tex] (0.5)

(x)=60

The correct answer is (c) 6/7 times 6/7 equals 36/49.

The correct evaluation for the exponential expression 6/7 to the power of 2 is (c) 6/7 times 6/7 equals 36/49.

To evaluate this expression, you need to multiply 6/7 by itself 2 times (since the exponent is 2). This gives you:

(6/7) to the power of 2 = (6/7) x (6/7) = 36/49

Therefore, the correct answer is (c) 6/7 times 6/7 equals 36/49.

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If triangle abc is an isosceles triangle with side lengths of 25, 25 and 48 centimeters, the area of triangle ABC is 600√(3) square centimeters.

To find the area of an isosceles triangle, we need to first determine the length of the altitude or height that is perpendicular to the base of the triangle.

In an isosceles triangle, the altitude divides the base into two equal parts, creating two right triangles. Using the Pythagorean theorem, we can find the length of the altitude.

Let x be the length of the altitude. Then, we have:

(25/2)^2 + x^2 = 25^2

625/4 + x^2 = 625

x^2 = 625 - 625/4

x^2 = 468.75

x = √(468.75)

x = 5√(75)

Now that we know the length of the altitude, we can find the area of the triangle using the formula:

Area = (1/2) x base x height

In this case, the base of the triangle is 48 cm and the height is 5sqrt(75) cm. Therefore, we have:

Area = (1/2) x 48 x 5√(75)

Area = 120√(75)

Area = 120 x 5√(3)

Area = 600√(3) cm^2

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Answer:

a = 9

Step-by-step explanation:

a ÷ 2 = [tex]\frac{9}{2}[/tex] ( express in fractional form )

[tex]\frac{a}{2}[/tex] = [tex]\frac{9}{2}[/tex] ( multiply both sides by 2 to clear the fractions ) , then

a = 9

The Tip cost for the meal is found as: $8.7975. The total cost of the meal is $67.4475.

'Percent' refers to a number that is 'out of 100. Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

At stores, online, in commercials, and in the media, you can see percentages practically anywhere. Understanding what percentages signify is a crucial skill that could help you save time as well as money and raise your employability.

Original cost of meal = $58.65

Tip cost = 15% of $58.65

Tip cost = 15*58.65 / 100

Tip cost = $8.7975

Total cost = Original cost of meal  + Tip cost

Total cost = $58.65 +  $8.7975

Total cost = $67.4475

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The data consists of 24 rows representing gender, admission status, and department for 4,526 applicants. The admission rate for men was 45%, for women was 30%, and the table of numbers is consistent with the given rates.

The data has a tabular structure with six rows corresponding to the six departments (A-F) and four columns representing the Gender, Admission status, Department, Count

The data is different from other datasets in that it provides information for each gender and admission status for each department separately. The 24 rows in the data set represent the different combinations of gender, admission status, and department.

The admission rate for all applicants is calculated by dividing the number of admitted applicants (1,755) by the total number of applicants (4,526), which gives an overall admission rate of approximately 0.387.

The admission rate for men is calculated by dividing the number of admitted men (1,493) by the total number of male applicants (3,356), which gives a male admission rate of approximately 0.445.

The admission rate for women is calculated by dividing the number of admitted women (1,262) by the total number of female applicants (1,670), which gives a female admission rate of approximately 0.301.

The table below summarizes the number of rejected and admitted applicants for each gender:

Gender Number Rejected    Number Admitted

Male          1863                 1493

Female         557                         1262

The numbers in the table are consistent with the given admission rates for men and women, as the admission rate for men is higher than that for women, and the number of male applicants is greater than the number of female applicants.

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_____The given question is incomplete, the complete question is given below:

Describe the structure of the data. Is it different than data you have examined before? Specifically, there are 24 rows in this data set, but the set provides information about 4,526 observations (the sum of the "count" column). Describe what each row represents. Each of the six departments (A-F) have four rows of data in this set corresponding to each of the following. 1st row Men who were admitted 9 . 2nd row Men who were not admitted . 3rd row Women who were admitted . 4th row Women who were not admitted . of the 4,526 applicants in this data set, 1,755 were admitted for an overall admission rate of approximately 39%. The admission rate for men was 45%, while the admission rate for women was 30%. Complete the following table. Gender Number Rejected Number Admitted 1198 Male 1493 ✓ Female 557 1278 Indicate how your numbers are consistent with these given admission rates for men and women. (Round your answers to four decimal places.)

From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.

A line segment having a single endpoint and an infinite length in one direction is known as a ray. A ray's length cannot be determined.

There are two endpoints to a line segment. Every point on the line connecting these endpoints to one another is also included. The length of a line cannot be measured, but the length of a segment can.

An eternally long and thin line is a group of points that stretches in two opposite directions.

From the given figure we observe that,

1. Two line segments are LA and EP.

2. Two rays are EC and AH.

3. Two lines are b and AP.

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Answer:

Z-0.15Z

Step-by-step explanation:

multiply z by the decimal form of 15, but since it's decreased by z you need to include a way of subtracting the z

The algebraic expression for the given statement is 0.85Z

An algebraic expression is a mathematical expression that consists of variables, numbers and operations.

Given that, Z decreased by 15%, we need to convert it into an algebraic expression

Multiply z by the decimal form of 15, but since it's decreased by z we will  subtract z from that,

So,

= Z - 15% of Z

= Z - 0.15Z

= Z(1-0.15)

= 0.85Z

Hence, the algebraic expression for the given statement is 0.85Z

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In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.

Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.

Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:

P(accurate order) = 1246 / 1300 = 0.958 for McDonald's

P(accurate order) = 1020 / 1100 = 0.927 Taco Bell

P(accurate order) = 708 / 800 = 0.885 for Burger King

P(accurate order) = 940 / 1000 = 0.94 for Wendy's

P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929

As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

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To find the area of the triangle with vertices (9,-1), (6,1), and (6,3), we can use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices.

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 9(1-3) + 6(3-(-1)) + 6((-1)-1) \right|$[/tex]

[tex]$A = \frac{1}{2} \left| -6 + 24 - 12 \right| = \frac{1}{2} \cdot 6 = 3$[/tex]

Therefore, the area of the triangle is 3 square units.

To find the area of the triangle with vertices (0,-8), (0,-10), and (7,-10), we can again use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 0((-10)-(-10)) + 0((7)-0) + 7((-8)-(-10)) \right|$[/tex]

$A = \frac{1}{2} \cdot 14 = 7$

Therefore, the area of the triangle is 7 square units.

To find the area of the triangle with vertices (6,-7), (3,-1), and (-1,4), we can again use the formula:

[tex]$A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$[/tex]

Plugging in the coordinates, we get:

[tex]$A = \frac{1}{2} \left| 6((-1)-4) + 3(4-(-7)) + (-1)((-7)-(-1)) \right|$[/tex][tex]$A = \frac{1}{2} \cdot 55 = \frac{55}{2}$[/tex]

Therefore, the area of the triangle is $\frac{55}{2}$ square units.

To find the area of the quadrilateral with vertices (-6,1), (-9,1), (-6,-4), and (-9,-4), we can divide it into two triangles and find the area of each triangle using the determinant method. The area of the quadrilateral is the sum of the areas of the two triangles.

First, we find the coordinates of the diagonals:

$D_1=(-6,1)$ and $D_2=(-9,-4)$

The area of the quadrilateral can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} -6 & 1 \ -9 & -4 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -9 & -4 \ -6 & -4 \end{array}\right|\

&=\frac{1}{2}\cdot 21 + \frac{1}{2}\cdot 9\

&=\frac{15}{2}\

\end{align*}

Therefore, the area of the quadrilateral is $\frac{15}{2}$ square units.

To find the area of the pentagon with vertices (0,3), (-3,3), (-5,1), (-3,-3), and (-1,-2), we can divide it into three triangles and find the area of each triangle using the determinant method. The area of the pentagon is the sum of the areas of the three triangles.

First, we find the coordinates of the diagonals:

$D_1=(0,3)$ and $D_2=(-1,-2)$

The area of the pentagon can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_3 & y_3 \ x_4 & y_4 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} 0 & 3 \ -3 & 3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -3 & 3 \ -5 & 1 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -5 & 1 \ -3 & -3 \end{array}\right|\

&=\frac{1}{2}\cdot 9 + \frac{1}{2}\cdot (-6) + \frac{1}{2}\cdot (-8)\

&=\frac{5}{2}\

\end{align*}

Therefore, the area of the pentagon is $\frac{5}{2}$ square units.

Area of triangle whose vertices are (6,1), (9,-1) and (6,-3) is 6 square units and the area of triangle whose vertices are (0,-8), (7,-10) and (0,-10) is 7 square units.

A polygon having 3 edges and 3 vertices is called a triangle. It is one of the fundamental geometric forms.

Lets find the area of triangle ( Pink Colour) whose vertices are (6,1), (9,-1) and (6,-3), [tex]Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ][/tex]

Area = 1/2 [ 6 ( -1 - (-3) ) + 9( -3 -1 ) + 6( 1 - ( -1 ) ) ]

Area = 1/2 [6 * 2 + 9 * (-4) + 6 * 2]

Area = 1/2 [12-36+12] = 1/2 (-12) = -6

Therefore , Area of Triangle is 6 square units.

Now, Lets find the area of triangle ( Brown Colour ) whose vertices are (0,-8), (7,-10) and (0,-10),

[tex]Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ][/tex]

Area = 1/2 [  0( -10 - ( -10 )) + 7 ( -10 - ( -8 ) ) + 0 ( -8 - ( -1- ) ) ]

Area = 1/2 [ 0 + 7 * (-2) + 0]

Area = 1/2 ( -14 ) = -7

Therefore, Area of Triangle is 7 square units.

Now. Lets find the area of Rectangle( Blue Colour ) whose length is 5 unit and Breadth is 3 unit.

So, Area of Rectangle = Length * Breadth

= 5 * 3 square units

= 15 square units.

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Answer: For 16 dozen cookies, Rachel used 24 cups of milk.

Step-by-step explanation:

We know that for each dozen cookies, Rachel uses 1 1/2 cups of milk. To find out how much milk she used for 16 dozen cookies, we need to multiply the amount of milk used for one dozen by 16. Here are the steps:

   Calculate the amount of milk used for one dozen cookies:

   1 1/2 cups of milk = 3/2 cups of milk

   For one dozen cookies, Rachel used 3/2 cups of milk.

   Multiply the amount of milk used for one dozen by 16:

   3/2 cups of milk x 16 = 24 cups of milk

Therefore, Rachel used 24 cups of milk for 16 dozen cookies.

If each dozen cookies Rachel used  [tex]1\frac{1}{2}[/tex]  cups of milk then 24 cups of milk she uses for 16 dozen cookies

Two or more expressions with an Equal sign is called as Equation.

Given that each dozen cookies Rachel used [tex]1\frac{1}{2}[/tex] cups of milk.

We have to find the number of cups of milk required to make 16 dozen cookies

As Rachel used  [tex]1\frac{1}{2}[/tex]  cups of milk for 1 dozen cookies.

She would use  [tex]1\frac{1}{2}[/tex]  x 16 = 24 cups of milk for 16 dozen cookies.

Hence, if each dozen cookies Rachel used  [tex]1\frac{1}{2}[/tex]  cups of milk then 24 cups of milk she uses for 16 dozen cookies

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The value οf the given angle x = 39.8 degree

Trigοnοmetry uses six fundamental trigοnοmetric οperatiοns. Trigοnοmetric ratiοs describe these οperatiοns. The sine functiοn, cοsine functiοn, secant functiοn, cο-secant functiοn, tangent functiοn, and cο-tangent functiοn are the six fundamental trigοnοmetric functiοns.

The ratiο οf sides οf a right-angled triangle is the basis fοr trigοnοmetric functiοns and identities. Using trigοnοmetric fοrmulas, the sine, cοsine, tangent, secant, and cοtangent values are calculated fοr the perpendicular side, hypοtenuse, and base οf a right triangle.

In the figure tanx = p/h

[tex]x = tan^{-1(15/18)}[/tex]

x = 39.8

Hence the value οf the given angle x = 39.8 degree

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Answer:

Assuming that (gof)(5) means (g(f(5))):

(gof)(5) = g(f(5)) = g(3x + 7) = 5x + 2

Therefore, (gof)(5) = 5(3x + 7) + 2 = 15x + 17.

Answer: Beth Blauer

Step-by-step explanation:

Answer:

Answer: C. f(x) = 2x²+x+6

a. The slope of AB is  [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. The mid-point of Diagonal AC is  [tex](0, -1/2)[/tex]

A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.

a.

Slope is given by

[tex]A = (-2, 3) and B = (-5, 0)[/tex]

[tex]m = 1[/tex]

[tex]B = (-5, 0) and C = (2, -4)[/tex]

[tex]m = -4/7[/tex]

Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex]  .

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y

Thus, Diagonal  [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]

Midpoint  [tex]= ((-2 + 2), (3 + -4))[/tex]

[tex]= ((0), (-1))[/tex]

Now divide them by 2

[tex]= ((0/2), (-1/2))[/tex]

[tex]= (0, -1/2)[/tex]

Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]

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Answer:

Step-by-step explanation:

To solve this problem, we will use the properties of the normal distribution and standardize the given value using the formula:

z = (x - μ) / σ

where:

x = 4.6 inches (the given value)

μ = 5 inches (the mean)

σ = 0.5 inches (the standard deviation)

So we have:

z = (4.6 - 5) / 0.5

z = -0.8

Now we need to find the probability that the standardized value is less than -0.8. We can use a standard normal distribution table or a calculator to find this probability.

Using a standard normal distribution table, we can look up the probability for z = -0.8, which is 0.2119.

Therefore, the probability that a randomly chosen item is less than 4.6 inches long is 0.2119 or approximately 21.19%.

The relative maximum of the function is (0, 4), and the relative minimum is (6, -152).

To find the relative extrema of the function f(x) = x^4 - 8x^3 + 4, we first take the derivative of the function:

f'(x) = 4x^3 - 24x^2

Then we set f'(x) = 0 to find the critical points:

4x^3 - 24x^2 = 0

4x^2(x - 6) = 0

This gives us two critical points: x = 0 and x = 6.

Next, we find the second derivative of f(x):

f''(x) = 12x^2 - 48x

We can use the Second-Derivative Test to determine the nature of the critical points.

For x = 0, we have:

f''(0) = 0 - 0 = 0

This tells us that the Second-Derivative Test is inconclusive at x = 0.

For x = 6, we have:

f''(6) = 12(6)^2 - 48(6) = 0

Since the second derivative is zero at x = 6, we cannot use the Second-Derivative Test to determine the nature of the critical point at x = 6.

To determine whether the critical points are relative maxima or minima, we can use the first derivative test or examine the behavior of the function around the critical points.

For x < 0, f'(x) < 0, so the function is decreasing.

For 0 < x < 6, f'(x) > 0, so the function is increasing.

For x > 6, f'(x) < 0, so the function is decreasing.

Therefore, we can conclude that the critical point at x = 0 is a relative maximum and the critical point at x = 6 is a relative minimum.

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