Exercise 1: 1) Suppose we have to select a manager, assistant manager, and night manager from a list of 11 people. How many ways can this be done

Based on Probability laws the answers are: (a) n(1-p) = 167.4 and (b) mean = 167.4

(a) To demonstrate that the probability distribution of X is roughly normal, we must determine if np and n(1-p), where n is the sample size and p is the chance of success, are both higher than or equal to 10. (using a variation of "lol").

If 55.8% of comments containing a textual form of laughter use some version of "lol," the numbers in this case are n = 300 and p = 0.558. Therefore:

[tex]n(1-p) = 300 * 0.442 = 132.6 np = 300 * 0.558 = 167.4[/tex]

The probability distribution of X is roughly normal since np and n(1-p) are both bigger than or equal to 10.

(b) The formula for the mean of the suitable normal distribution is: = np = 300 x 0.558 = 167.4.

Hence, 167.4 is the normal distribution's mean.

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Step-by-step explanation:

To simplify the expression x^-2y(x^3y^5)^3, we need to perform the operations inside the parentheses first, using the exponent rule that (a^m)^n = a^(mn):

x^-2y(x^3y^5)^3 = x^-2y(x^(33)y^(53)) = x^-2y(x^9y^15)

Next, we can simplify the expression by multiplying the coefficients (numbers) and adding the exponents of x and y, using the product rule that x^mx^n = x^(m+n) and (xy)^m = x^my^m:

x^-2y(x^9y^15) = (1y/x^2)(x^9*y^15) = y^(15+1)x^(9-2) = y^16x^7

Therefore, the simplified form of x^-2y(x^3y^5)^3 is y^16*x^7.

Note that this expression is defined for all values of x and y except for x=0.

Answer:

logra =70000

queda=90000

Step-by-step explanation:

additional

total income 70000+90000=160000

division by 2

160000/2

=$80.000

The vertices of the image of triangle ABC under the transformation (x, y)-- (x-3,y+1) followed by a dilation centered at the origin with scale factor 2 are A(2(x1-3),2(y1+1)), B(2(x2-3),2(y2+1)), C(2(x3-3),2(y3+1)).

Transformation in maths is the process of changing the position, size, orientation or shape of a figure or shape. It involves various techniques such as translation, rotation, reflection and scaling.

The transformation (x, y)-- (x-3,y+1) followed by a dilation centered at the origin with scale factor 2 is a combination of a translation and a dilation. A translation is a transformation that moves the shape without changing its size or orientation. In this case, the translation moves the triangle 3 units to the left and 1 unit up. A dilation is a transformation that enlarges or reduces a shape. In this case, the dilation uses a scale factor of 2, so the triangle will be twice as big as it was before.

The vertices of the original triangle ABC are (A(x1,y1), B(x2,y2), C(x3,y3)). After the translation, the vertices will be (A(x1-3,y1+1), B(x2-3,y2+1), C(x3-3,y3+1)). After the dilation, the vertices will be (A(2(x1-3),2(y1+1)), B(2(x2-3),2(y2+1)), C(2(x3-3),2(y3+1)).

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The inequality x ≤ 3 indicates how many different bicycle outfits she can purchase.

She has $560 to spend at a bike shop on new accessories and clothing for riding.

For $425.05. she spends on a brand-new bicycle.

She spends $15.19 for each of four bicycle reflectors and $15.79 on a pair of cycling gloves.

She intends to use all or part of the remaining funds to purchase new bicycle clothing at $29.20 each.

The disparity that can be used to calculate how many garments she can purchase for her budget is as follows:

let

x = the number of garments

Therefore,

425.05 + 15.19(4) + 15.79 + 29.20x ≤ 560

425.05 + 60.76 + 15.79 + 29.20x ≤ 560

29.20x ≤ 560 - 425.05 - 60.76 - 15.79

29.20x ≤ 58.4

Divide the difference between the two sides by 29.20.

x ≤ 58.4 / 19.20

x ≤ 3.04166666667

x ≤ 3

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The properties used to simplify the expression are given as follows:

In algebra, the combination of like terms refers to the process of simplifying expressions by adding or subtracting terms that have the same variable(s) raised to the same power(s).

In this problem, from step 1 to step 2, on the left side of the equality, all the terms with the variable n and exponent 1 were added, as were the constant terms, hence the like terms were combined.

In Step 4, the variable n was obtained applying the division operation, which is the inverse operation of the multiplication operation in Step 3.

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Answer:

y = - 9x + 6

Step-by-step explanation:

the equation of a linear function in slope- intercept function is

y = mx + c ( m is the slope and c the y- intercept )

given slope = - 9 and f(0) = 6 , that is the point (0, 6 ) , then c = 6

y = - 9x + 6 ← linear function

Volume, it is defined as the space occupied within the boundaries of any three-dimensional solid.

Volume is defined as a capacity occupied or captured by a 3-dimensional solid shape. It is difficult to visualise in any shape, yet it may be compared amongst shapes. For instance, a geometry box has a larger or bigger volume than an eraser placed inside of it. We split the area into equal square units to determine or get the area of any 2-dimensional form.

Cuboid, is a 6-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid is short for "like a cube".

[tex]Volume\ of \ Cuboid = Length * Breadth * Height[/tex]

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answer: 10

y = |2| + 8

y = 2 + 8

y = 10

Since an actual mosquito is about 1.6 cm, the scale factor of the diagram is equal to 2.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (actual figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image (actual figure)

Conversion:

1 cm = 10 mm

1.6 cm = 1.6 × 10 = 16 mm.

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = 32/16

Scale factor = 2.

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Answer:

1483 pedro 1203 ricky

Step-by-step explanation:

1203+1483 = 2686

a) The percentage of adults in the USA that have stage 2 high blood pressure is; 0.27%

b) The number of people that you will expect to have BP greater than 160 is; 54

a) if x is systolic blood pressure, then want to find probability that x ≥ 160.

The formula for z-score is;

z = (x - mean)/standard deviation

Thus;

z = (x - 119)/18

This is normally distributed with mean 0 and standard deviation 1

Transform x to z:

P(x > 160) = P(z > (160 - 119)/18)

= P(z > 2.78)

= P(z < -2.78)

= 0.0027 (from standard normal distribution table, which 0.27%.)

b)  Since probability of BP > 160 is 0.027.  

Then out of 2000 people, then 2000 * 0.027 = 54 people would have BP > 160.

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Therefore , the solution of the given problem of area comes out to be the rectangle's dimensions are 6.5 yards and 10 yards, respectively.

By calculating how much space would be needed to fully cover its exterior, its overall size can be calculated. The neighboring area is considered when selecting a comparable item for a rectangular design. The surface area of something determines its overall dimensions. The number of sides between a cuboid four trapezoidal curves determines how much water it can hold.

Here,

Let w represent the rectangle's breadth.

In light of the issue statement, the rectangle's length is 2w - 3.

Since the rectangle's area is 65, we can construct the following equation:

=> w(2w - 3) = 65

By enlarging and condensing the left half, we obtain:

=>2w² - 3w - 65 = 0

Now that we have the quadratic formula, we can answer this quadratic equation:

=> w = (-b √(b² - 4ac)) / 2a.

where c = -65, b = 3, and a = 2. By replacing these numbers, we obtain:

=> w = (-(-3) ± √(-3)² - 4(2)(-65))) / 2(2)

=> w = (3 + √(529)) / 4

=> w = (3 ± 23) / 4

=> w = (3 + 23) / 4 = 6.5

=> l = 2w - 3 = 2(6.5) - 3 = 10

The rectangle's dimensions are 6.5 yards and 10 yards, respectively.

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Answer:

D) PR and CK form right angles

Step-by-step explanation:

⟂ is the symbol for a perpendicular, so it is a perpendicular bisector.

- Perpendicular bisectors divide an angle into 2 90° angles.

Answer:

4

Choice D

Step-by-step explanation:

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\dfrac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]

[tex]\mathrm{Periodicity\:of\:}\cos \left(x\right)\:\mathrm{is}\:2\pi[/tex]

To predict the average number of people attending local baseball games in 2024, we need to use the formula:

A = P(1 + r)^n

where:

A = the predicted average attendance in 2024

P = the current average attendance (in 2020)

r = the annual growth rate (as a decimal)

n = the number of years of growth (from 2020 to 2024)

Given that the annual growth rate is 10% and the number of years of growth is 4 (from 2020 to 2024), we have:

r = 0.10

n = 4

Substituting these values and the current average attendance of 100 people into the formula, we get:

A = 100(1 + 0.10)^4

A = 100(1.10)^4

A = 100(1.4641)

A = 146.41

Therefore, the predicted average number of people attending local baseball games in 2024 is approximately 146 (rounded to the nearest whole number).

Answer:

54 square meters

Step-by-step explanation:

Given the scale is 1 centimeter represents 3 meters, to scale the dimensions of the drawing to the dimensions of the actual room, multiply the dimensions of the drawing by 3.

Therefore:

So the dimensions of the actual room are:

The area of a rectangle is the product of its width and length.

Therefore, the area of the actual room is:

The  surface area of the prism 1 is 56.25( optionC)

Similar shapes are shapes with thesame shape but not necessarily thesame side.

The ratio of the corresponding sides of prism 1 to prism 2 = 5/12

therefore 5/12 is the linear scale factor.

The area factor is the square of linear scale factor .

Therefore area factor = (5/12 )² = 25/144

To find the area of prism 1, we use the area factor.

Represent the area of prism 1 by x

25/144 = x/ 324

144x = 324 × 25

144x = 8100

divide both sides by 144

x = 8100/144

x = 56.25

therefore the area of prism 1 is 56.25

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Using geometry, we can find that the length of the line segment AC as per the distance between two points is= 18 ft.

What are line segments?

In geometry, a line segment's borders are determined by two distinct points on the line. Any portion of a line that connects two places is referred to as a line segment.

A segment has an endpoint, whereas a line doesn't.

What are some examples of line segments in the real world?

a scale, a ruler, a stick, and a boundary line.

Thus, the length of the line segment AC is = 18ft.

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The length of side BC is solved to be 24 units

The problem gave that the two triangles are similar triangles and the proportions will be used to find the length of BC as below

5 / (x - 4) = (x + 7) / 12

cross multiplying

60 = (x - 4) (x + 7)

60 = x^2 + 3x - 28

x^2 + 3x - 88 = 0

x = 8 or -11

take the positive value hence x = 8

Solving for BD

side DE = x - 4 = 8 - 4 = 4

taking proportions we have

DE / FE = AB / BC

4 / 8 = 12 / BC

BC = 8 * 12 / 4 = 24

therefore length of BC is equal to 24 units

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The figure which could not be a cross section of a right circular cone is option a and d.

A right circular cone is a three-dimensional geometric shape that has a circular base and a vertex directly above the center of the base, such that the axis passing through the vertex and the center of the base is perpendicular to the base.

The base of the cone is a circle, and the sides of the cone slope upward to meet at the vertex. The distance from the vertex to the center of the base is called the height of the cone, denoted by h, and the distance from the center of the base to any point on the edge of the base is called the radius, denoted by r.

The lateral surface of the cone is curved, while the base and the vertex are flat. The angle formed between the height and the slant height (the distance from any point on the base to the vertex) is called the half vertical angle or the apex angle of the cone, denoted by θ.

The formula for the volume of a right circular cone is given by V = (1/3)πr²h, while the formula for the lateral surface area of a right circular cone is given by L = πrℓ, where ℓ is the slant height of the cone, which is equal to √(r² + h²).

Circle and eclipse cannot be cross section of a right circular cone.

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Circumradius of the isosceles triangle = 20 units

A triangle with two sides that have the same length is said to be isosceles. Let's carry out a quick exercise to better comprehend this. Fold the corners of a rectangular piece of paper in half. From the top folded corner to the bottom border, draw a line. O, D, and C should be noted as the triangle's vertices.

Now quantify the OD and OC. Use several measures to perform this exercise again and look for patterns. It is evident that OD and OC are consistently  isosceles triangle. An isosceles triangle is a triangle with equal-lengths on both sides.

Now here circumradius, r = abc/√ [(a+b+c)(a+b-c)(a+c-b)(b+c-a)]

r = 29× 29 × 40/ √ (98×18×40×40)

= 29×29/42

≈20.02

=20

Hence the circumradius of the given triangle is 20 units.

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The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is 27/8 square inches or 3 3/8 square inches

From the question, we are to determine the area of the cross-section of the cone

To determine the area of the cross-section of the cone, we will determine the radius of the cross-section.

Let the radius of the cross-section be x and radius of the base of the be r.

The height of the cone is 8 inches and the height of the cone formed from the cross-section is 3 inches

By similar triangle theorem, we can write that

8/r = 3/x

x = (3r)/8

From the given information,

The area of the base is 24 square inches

Thus,

πr² = 24

Therefore, r² = 24/π

The area of the cross-section will be

A = πx²

But, x = (3r)/8

Thus,

A = π [(3r)/8]²

A = π × 3²/8² × r²

A = π × 9/64 × 24/π

A = 27/8 square inches

Hence, the area is 27/8 square inches or 3 3/8 square inches

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Yοur friend's statement is nοt cοrrect.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Nο, yοur friend's statement is nοt cοrrect.

The reasοn is that the twο temperatures are measured using different scales. The temperature inside the building is given in Celsius (°C), while the temperature οutside is given in Fahrenheit (°F). These are twο different scales, and a temperature οf 22°C is nοt equal tο a temperature οf 22°F.

Tο cοmpare the twο temperatures, we need tο cοnvert οne οf them tο the οther scale. One way tο dο this is tο use the cοnversiοn fοrmula:

°F = (°C × 9/5) + 32

Using this fοrmula, we can cοnvert the temperature inside the building frοm Celsius tο Fahrenheit:

°F = (22°C × 9/5) + 32 = 71.6°F

Nοw we can see that the temperature inside the building is much higher than the temperature οutside the building.

Hence, yοur friend's statement is nοt cοrrect.

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Answer:

RESOLUCIÓN.

Para resolver este problema hay que seguir los siguientes pasos:

1) Determinar la comisión del vendedor de seguros.

Se sabe por datos del problema que cuando vendió $3000 su sueldo total fue de $850 y cuando vendió $4000 su sueldo total fue de $1000, eso quiere decir que:

Venta = 4000 - 3000 = $1000

Sueldo = 1000 - 850 = $150

Es decir que por cada $1000 en ventas, su ganancia es de $150.

1000 ---> 100%

150 ---> x

x = 150 * 100 / 1000 = 15%

Por lo tanto el porcentaje de comisión del vendedor es de 15% por venta.

2) Determinar el salario semanal fijo del vendedor.

Una vez conocido el porcentaje de comisión se puede obtener el salario fijo.

Para el primer caso:

850 = Salario fijo + Comisión

Comisión = 3000 * 15/ 100 = $450

Por lo tanto se tiene que:

850 = Salario fijo + 450

Salario fijo = $400

Por lo tanto se tiene que el salario semanal del vendedor es de $400.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The statement "85% of 'a' is 'b'" can be represented mathematically as:

0.85a = b

This means that 'b' is 85% of 'a'.

To answer the question:

a = b/0.85

So, a is equal to 'b' divided by 0.85.

Therefore, the correct option is (a) a=b.

Answer:

The principal square root of a non-negative real number is the positive square root. For example, the principal square root of 25 is 5, since 5^2 = 25.

When solving radical polynomials, the principal square root is used because it is the most commonly used square root. In many contexts, including mathematical and scientific calculations, the principal square root is the default choice unless otherwise specified. Additionally, when working with radical expressions, we often simplify expressions by taking the principal square root, as it can help us to simplify calculations and express answers more clearly.

Answer:

Frequency distributions are visual displays that organize and present frequency counts so that the information can be interpreted more easily.

Step-by-step explanation:

The distribution of a variable is the pattern of frequencies, meaning the set of all possible values and the frequencies associated with these values.

The range of lengths Brett can use for the third piece of steel is 4 in. < x < 20 in.

The Triangle is a polygon with three line segments as its boundaries. That is the tiniest polygon imaginable. Three vertices, three internal angles, and three sides make up a triangle.

The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for every triangle, the sum of the lengths of the first two sides is always higher than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

Using the triangle inequality theorem we have:

8 + 12 > x

x + 8 > 12

x + 12 > 8

20 > x

x > 4

x > -4

Therefore, the range of lengths Brett can use for the third piece of steel is 4 in. < x < 20 in.

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