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value of side x in the triangle is 6 ( simplest radical form with a rational denominator is 6/1).

A right triangle is a triangle that has one angle measuring 90 degrees, which is also called a right angle. The hypotenuse is the side that faces the right angle, while the legs are the other two sides.

Trigonometric functions are a set of mathematical functions used to relate the angles and sides of a right triangle. Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six fundamental trigonometric functions (cot).

In the given right angles triangle

Using trigonomteric function

Tan30°=√12/x

1/√3=√12/x

x=√12×√3

x=√36

x=6

Hence, value of side x in the triangle is 6.

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The area of triangle in given figure is = 60 cm²

A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane.The sum of the interior angles of a triangle is always 180 degrees, and the length of each side can be determined by the application of the Pythagorean theorem or other trigonometric functions, depending on the given information. Triangles can also be classified based on the size of their angles and the lengths of their sides, which give rise to various types of triangle such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

According to quesrtion

Given height = 3cm

Base = 10cm

if the height is quadrupled then height = 4 × 3 = 12cm

Area = 1/2 × base × height

= 1/2 × 70 × 12

to solve this we get

Area = 60cm²

So, the area of this triangle is 60cm²

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Direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.

What is direct variation equation?

A direct variation equation is a mathematical equation that describes a relationship between two variables that varies proportionally. In other words, if one variable increases or decreases, the other variable also increases or decreases in proportion to it.

Given, S varies directly as t, and S = 8 when t = 16.

Let's find the constant of variation (k) using the given information:

k = S/t = 8/16 = 0.5

So, the constant of variation is 0.5.

Using the constant of variation, we can write a direct variation equation relating s and t as:

S = kt

Substituting k = 0.5 in the above equation, we get:

S = 0.5t

When S = 16, we can find t as follows:

16 = 0.5t

t = 16/0.5

t = 32

Therefore, when S = 16, t = 32.

Therefore, direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.

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Answer: 24,500 ways

Step-by-step explanation:

The number of ways to select 4 appetizers out of 8 is given by the combination C(8,4) = 70. Similarly, the number of ways to select 3 main courses out of 5 is given by C(5,3) = 10, and the number of ways to select 3 desserts out of 7 is given by C(7,3) = 35.

To find the total number of ways to select the full meal consisting of 4 appetizers, 3 main courses, and 3 desserts, we can use the multiplication principle of counting, which states that the total number of ways to perform a sequence of independent tasks is equal to the product of the number of ways to perform each individual task.

Therefore, the total number of ways to select the full meal is given:

70 x 10 x 35 = 24,500

Hence, there are 24,500 ways to select 4 appetizers, 3 main courses, and 3 desserts from the given options.

Answer:

Step-by-step explanation:

The number of ways to select 4 appetizers out of 8 is given by the combination C(8,4) = 70.
Similarly, the number of ways to select 3 main courses out of 5 is given by C(5,3) = 10, and the number of ways to select 3 desserts out of 7 is given by C(7,3) = 35.

To find the total number of ways to select the full meal consisting of 4 appetizers, 3 main courses, and 3 desserts, we can use the multiplication principle of counting, which states that the total number of ways to perform a sequence of independent tasks is equal to the product of the number of ways to perform each individual task.

Therefore, the total number of ways to select the full meal is given:70 x 10 x 35 = 24,500.

Hence, there are 24,500 ways to select 4 appetizers, 3 main courses, and 3 desserts from the given options.

Answer:

To find the slope between two points (x1, y1) and (x2, y2), we use the formula:

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

Using the given points P(-11, -24) and Q(21, 40), we can substitute the values into the formula:

slope = (40 - (-24)) / (21 - (-11))

slope = 64 / 32

Therefore, the slope between points P(-11, -24) and Q(21, 40) is 2.

Answer:

2

Step-by-step explanation:

To find the slope, we can use the slope formula

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

    = ( 40 - -24)/(21 - -11)

    = ( 40+24)/(21+11)

    = 64/32

    = 2

Answer: y= -6

Step-by-step explanation: use the slope formula and slope intercept; y=mx+b

Answer: 15.4% (rounded to the nearest tenth)

Step-by-step explanation:

The number which could be added to both sides of the quadratic equation to complete the square is; -2.25.

What in mathematics is a quadratic equation?

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complicated solutions are also possible.

The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;

1 - 2.25 = (x -3/2)² - 2.25

Hence, the number which should be added to both sides of the equation is; -2.25.

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The chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.

A statistics teacher wants to know if the student birth month is distributed equally across all months. He uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test this hypothesis.

This is not an appropriate use of a chi-square goodness-of-fit test because chi-square goodness-of-fit tests are used to compare the distribution of categorical data to a theoretical distribution.

The chi-square goodness-of-fit test compares observed frequencies of categorical data to expected frequencies based on a theoretical distribution. It is used to determine if a sample of data comes from a specific population or not.

In this case, the teacher is not comparing observed frequencies to expected frequencies, but instead is testing the hypothesis that the distribution of student birth months is equal across all months.

This is not a proper use of a chi-square goodness-of-fit test because the hypothesis being tested is not related to the expected frequencies of a categorical variable. Therefore, the chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.

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To given expression |x + 3| simplifies solution is x + 3.

What is expression?

In mathematics, an expression is a combination of symbols, numbers, and operators that represent a quantity or a mathematical relationship. It can be a single number or a combination of numbers, variables, and operators that can be evaluated to give a numerical result.

If x > 2, then the expression |x + 3| can be simplified as follows:

|x + 3| = x + 3

since x + 3 is already non-negative when x > 2.

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The first, second, and third one.

Answer:

the solution for x is (53 - b)/a.

Emily has to pay $41.31 for the shirt after adding coupon and discount.

How to find the Cost Price (CP) of any discounted item?

Lets say CP = 54 and the discount is of 15% i.e. marked price

So, Marked Price= 85% of CP = 45.9

Lets apply the additional coupon of 10% on Marked Price.

Therefore, the payment amount = 90% of MP

payment amount = $41.31

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The area of a triangle whose sides have lengths √70,√70,√and 28 is 10.45.

What is the area of the triangle?

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle =  (0.5)x b x h

Length of its base = b units

Its height = h units long,

Given;

The sides of the triangle √70,√70,√28

Now,

H²=70-28/4

H²=70-7

H=7.9

[tex]Area= b *\frac{ h}{2}[/tex]

[tex]=\sqrt{28}\frac{7.9}{2}[/tex]

=10.45

Therefore, the area of the triangle will be 10.45.

The complete question is-

What is the area of a triangle whose sides have length √{70},√{70}, and √{28} ?

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Answer:

AB = 6.71 to nearest hundredth.

Step-by-step explanation:

To get from A to B we move 3 units to the right then 6 units up.

This form a right angled triangle so we use Pythagoras theorem:

AB^2 = 3^2 + 6^2

         =  9 + 36

         = 45

So AB = √45

           = 3√5  = 6.7082

Answer:

The outlier in this graph is (4, 55)

Step-by-step explanation:

Outliers can be seen graphically when we first draw a line of best fit. When we draw the line of best fit it connects through the middle of the string of points near the top of our graph. We can see that any given point on the graph is either on the line of best fit or very close to it. This can be said about all points but one... the point (4,55). This point lies far away from the line we've created and can be identified as an outlier for this reason.

Answer:

13

Step-by-step explanation:

Evaluate the expression:

[tex]6-(5 \div a)^3 +8[/tex]

a = 5, plug in the value

[tex]6-(5\div 5)^3 + 8[/tex]

Divide in parentheses

[tex]6-1^3+8[/tex]

1^3 = 1, then subtract 6 and 1

[tex]5+8[/tex]

Add

[tex]13[/tex]

Answer:

Therefore, the staff should order 320 blue bags, 360 black bags, and 120 gray bags.

Step-by-step explanation:

To determine how many bags of each color to order, we need to estimate the proportion of students who prefer each color based on the sample of 120 students. We can then use these proportions to predict the number of bags of each color needed for all 800 students. Here's how we can do it:

Determine the number of students in the sample who prefer each color:

Let B be the number of students who prefer blue

Let K be the number of students who prefer black

Let G be the number of students who prefer gray

Based on the sample of 120 students, we know:

B + K + G = 120

Estimate the proportion of students who prefer each color:

The proportion of students who prefer each color in the sample is:

p(B) = B/120

p(K) = K/120

p(G) = G/120

Predict the number of bags of each color needed for all 800 students:

The predicted number of bags of each color needed for all 800 students is:

Bags of blue = p(B) * 800

Bags of black = p(K) * 800

Bags of gray = p(G) * 800

So, using the sample results, we get:

Bags of blue = (48/120) * 800 = 320

Bags of black = (54/120) * 800 = 360

Bags of gray = (18/120) * 800 = 120

The given wood length does not satisfied the property of triangle through which it unable to create a triangle.

What about length of triangle?

The length of a triangle depends on the specific triangle you are referring to and the measurements of its sides. A triangle is a three-sided polygon, and its length is typically measured as the length of its sides.

There are different types of triangles based on their side lengths, such as equilateral triangles with three equal sides, isosceles triangles with two equal sides, and scalene triangles with no equal sides. The length of each side in these triangles can be determined using various methods, such as the Pythagorean theorem, the Law of Cosines, or trigonometric functions.

Define triangle property:

A triangle is a polygon with three sides and three angles. The properties of a triangle include:

According to the given information:

As, we know the property of triangle that sum of two side always greater than third side of the triangle. But when add 16 inch and 14 inch we get 30 inch as a result that is same length of the third side.

Hence, it is not greater than third side so, through the given length we can't create a triangle.

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Answer:

187,550,190

Step-by-step explanation:

The type of control chart should be used here is equals to C-chart. So, the right answer is option (c). The upper and lower control limits are 10 and 0 respectively.

We have a quality style manufactures self-assembling furniture.

Average Defect rate = 4 per day

Now, here we are checking the number of defective packages per day which is independent day to day and have a mean or average of 4 per day. So, we use here the C- chart one of type of control chart. Also, we have to draw control chart with 3-sigma control limits. Average defect Rate, c' = 4

We determine the control limits,

CL = 3 ( 3-sigma )

The upper control limit , UCL = c' + 3 √c'

= 4 + 3 √4 = 10

The lower limit, LCL= max ( 0, c' - 3 √c')

c' - 3 √c' = 4 - 3√4 = -2, as it is less than zero, So, lower control limit, LCL= 0.00.

The construction of control chart always consists,

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Complete question:

quality style manufactures self-assembling furniture. to reduce the cost of returned orders, the manager of its quality control department inspects the final packages each day using randomly selected samples. the defects include wrong parts, missing connection parts, parts with apparent painting problems, and parts with rough surfaces. the average defect rate is four per day. owhich type of control chart should be used?

i) R chart

ii) p chart

iii) c chart

construct a control chart with 3-sigma control limits.

The population of bacteria after I days is P(I) = 3700 * e^(0.11 * I) and  percentage rate of change per hour is 0.4285%

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

The population of bacteria in the petri dish is growing exponentially at a rate of 11% per day. This means that the daily growth rate r is 0.11, or 11/100.

The formula for exponential growth is:

P(t) = P0 * e^(rt)

Where:

P(t) is the population after t days

P0 is the initial population

r is the growth rate per day

e is the mathematical constant approximately equal to 2.71828

Using the given information, we have:

P0 = 3700

r = 0.11

So, the formula for the population of bacteria after I days is:

P(I) = 3700 * e^(0.11 * I)

To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. There are 24 hours in a day, so the hourly growth rate h is:

h = (1 + r)^(1/24) - 1

Substituting the value of r, we get:

h = (1 + 0.11)^(1/24) - 1

Simplifying this expression, we get:

h = 0.004285

So, the hourly growth rate is 0.4285%, or 0.004285 expressed as a decimal.

Therefore, the population of bacteria after I days is:

P(I) = 3700 * e^(0.11 * I)

And the percentage rate of change per hour is:

0.4285% (rounded to the nearest hundredth of a percent)

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The percentage rate of change per hour is approximately 0.46%.

How to calculate percentage?

The formula for exponential growth is:

N(t) = N0 * e raise to the power (r*t)

where:

N(t) is the population at time t

N0 is the initial population

r is the growth rate

e is the mathematical constant approximately equal to 2.71828

t is the time elapsed

In this case, we have:

N0 = 3700

r = 11% per day, or 0.11/24 = 0.0045833 per hour (since there are 24 hours in a day)

t is the time elapsed in days

To convert the time elapsed in days to hours, we can multiply t by 24. Therefore, the function for the population of bacteria after t days is:

f(t) = 3700 * e raise to the power (0.004583324t)

To round the coefficients in the function to four decimal places, we can use the round() function in Python:

f(t) = round(3700 * e**(0.004583324t), 4)

To determine the percentage rate of change per hour, we can calculate the percentage increase in the population per hour using the formula:

Percentage increase = (e raise to the power (r*h) - 1) * 100

where:

r is the growth rate per day

h is the time elapsed in hours

In this case, we have:

r = 11% per day, or 0.11/24 = 0.0045833 per hour

h = 1 hour

Plugging these values into the formula, we get:

Percentage increase = (e raise to the power (0.0045833*1) - 1) * 100 = 0.4646%

Therefore, the percentage rate of change per hour is approximately 0.46%.

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Step-by-step explanation:

Height = - 16 t^2  + 96 t + 4

   max will occur at   t =  - b/2a   =   -  96/(2*-16) = 3 seconds

The max height at t = 3

   Height = -16 (3^2) + 96 (3) + 4 = 148 ft

Answer:

the final answer is 80800 exactly

Answer: $80 880 US$

Step-by-step explanation:

Add all up

Answer:

Step-by-step explanation:

The probability that Sean will make more than Evan on a randomly selected week is approximately 0.3446 or 34.46%.

To calculate the probability that Sean will make more than Evan in a randomly selected week, we need to compare their incomes in terms of standard deviations from the mean.

First, we need to calculate the difference between their means:

Mean difference = Sean's mean income - Evan's mean income = $225 - $240 = -$15

Next, we need to calculate the standard deviation of the difference between their incomes:

Standard deviation of difference = √[(Sean's standard deviation)^2 + (Evan's standard deviation)^2] = √[(35)^2 + (15)^2] = 37.42

Now, we can use a z-score table to find the probability that Sean's income will be higher than Evan's income:

Z-score = (Sean's income - Evan's income - Mean difference) / Standard deviation of difference = (225 - 240 - (-15)) / 37.42 = 0.40

From the z-score table, we find that the probability of a z-score of 0.40 or higher is 0.3446.

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Answer:mason must need 33.6 m of materail to make  8 curtains.

so he need to 17.6m of material

Step-by-step explanation:

The measure of following values for the given circle is:

Sector AE = (2/3)π square units

Sector AB = (10/9)π square units

Sector ECB = (1/3)π square units

Angle BOC = 160 degrees

In geometry, a circle is a two-dimensional shape that is defined as the set of all points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius of the circle.

Here,

Sector AE:

The central angle of 60 degrees represents one-sixth (60/360) of the circle, so the sector AE has an area of one-sixth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AE is:

(1/6) x 4π = (2/3)π square units

Sector AB:

The central angle of 50 degrees represents 5/18 (50/360) of the circle, so the sector AB has an area of 5/18 of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AB is:

(5/18) x 4π = (10/9)π square units

Sector ECB:

Since angles EOC and BOC are complementary (they add up to 90 degrees), the central angles they subtend are also complementary. Therefore, the central angle of sector ECB is 90 - 60 = 30 degrees. This represents one-twelfth (30/360) of the circle, so the sector ECB has an area of one-twelfth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector ECB is:

(1/12) x 4π = (1/3)π square units

Angle BOC:

Since angles AOB and COE are both right angles (as they subtend diameters of the circle), we know that angle AOC is 90 degrees. Therefore, angle BOC is:

360 - 90 - 60 - 50 = 160 degrees

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The amount Mariano must make from his job is

$2,500 ($12,500 * 0.2) =  $2500.

A number can be divided by five or multiplied by 0.2 to determine 20% of that amount.

Mariano, for instance, would have to pay $12,500 ($15,000 - $800 - $1,700)

if he had to pay $15,000 for a year of classes at the University of Texas at Brownsville but had also been awarded a grant for $800 and a scholarship for $1,700.

We can divide $12,500 by 5 or multiply it by 0.2 to calculate how much he must make from his employment to cover 20% of the remaining expenses.

The amount Mariano must make from his job is

$2,500 ($12,500 * 0.2) =  $2500.

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