Question 46 of 50
Congruent figures are:

figures that are exactly the same size and shape.

figures that are the same shape.

figures that are the same size.

The standard deviation of the variable "Defects in batch" is approximately 0.47.

The closest answer in the options is (C) 1.51.

The standard deviation is described as a measure of the amount of variation or dispersion of a set of values.

Standard Deviation is given as  = √(sum(p(x - μ)^2) / n)

Where μ = sum(xp)

= 2 * 0.35 + 3 * 0.23 + 4 * 0.20 + 5 * 0.09 + 6 * 0.07 + 7 * 0.06

= 2.49

substituting the values into the standard deviation formula, we have :

SD = √(sum(p(x - μ)^2) / n)

= √((0.35 * (2 - 2.49)^2 + 0.23 * (3 - 2.49)^2 + 0.20 * (4 - 2.49)^2 + 0.09 * (5 - 2.49)^2 + 0.07 * (6 - 2.49)^2 + 0.06 * (7 - 2.49)^2) / 6)

= √(1.32 / 6)

= √(0.22)

= 0.47

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The standard deviation of this variable is given as follows:

1.51.

Before obtaining the standard deviation, we must obtain the expected value, which is given by the sum of each value multiplied by it's respective probability, hence:

E(X) = 2 x 0.35 + 3 x 0.23 + 4 x 0.20 + 5 x 0.09 + 6 x 0.07 + 7 x 0.06

E(X) = 3.48.

Then we obtain the sum of the differences squared between each observation and the mean, multiplied by it's respective probabilities, hence:

(2-3.48)² x 0.35 + (3-3.48)² x 0.23 + (4-3.48)² x 0.20 + (5-3.48)² x 0.09 + (6-3.48)² x 0.07 + (7-3.48)² x 0.06 = 2.2696.

The standard deviation is the square root of this sum, hence:

S(X) = sqrt(2.2696)

S(X) = 1.51.

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Solving a system of equations we wll see that there are  are 24 women, and the other 15 students are men in foruth grade.

We know that there are 39 students in fourth grade, we know that:

3/4 of the women went

2/3 of the men went

And this leaves 11 students at the school, then we can write the equation:

(3/4)*W + (2/3)*M + 11 = 39

Where W and M are the number of women and men respectively.

(3/4)*W + (2/3)*M = 39 - 11  = 28

(3/4)*W + (2/3)*M = 28

And we also know that the total number is 39, then:

M + W = 39

So we can write the system of equations:

(3/4)*W + (2/3)*M = 28

M + W = 39

M = 39 - W

REplacing that on the other equation we get:

(3/4)*W + (2/3)*(39 - W) = 28

(3/4)*W - (2/3)*w + 26 = 28

(3/4)*W - (2/3)*W = 28 - 26 = 2

(9/12)*W - (8/12)*W = 2

(1/12)*W = 2

W = 2*12 = 24

There are 24 women, and the other 15 students are men.

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The distance covered by the jack is 1.5 miles.

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

Given  Jack jogged 2 - 5/10 miles on a path in the park.

2 - 5/10 miles

convert 5/10 in decimal form,

5/10 = 0.5

subtract 0.5 from the equation,

so 2 - 5/10 miles =  2 - 0.5 = 1.5 miles

2 - 5/10 miles = 1.5 miles

Hence distance in decimal is 1.5 miles.

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The diameter of the back wheel is 18 in.

A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.

Given that, a model had a front wheel with a 52 in. diameter and one spoke on the back wheel measuring 9 in, we need to find the diameter of the back wheel.

Since, the spoke in a wheel will act as a radius of the wheel,

Radius = diameter / 2

Also, it is given that, the one spoke on the back wheel measuring 9 in,

Therefore, the diameter of the back wheel = 9 × 2

= 18 in

Hence, the diameter of the back wheel is 18 in.

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The complete question:

If the arc measure of MN = 87°, what is the measure of angle ∠MON ?

Solution:

In the given circle, the required measure of the angle ∠MON is given as 87°.

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Here,

For the given circle, the measure of arc MN is given in the form of an angle of 87° which consists of an angle MNO,

So the measure of the section is equal to MON i.e. ∠MON = 87°

Thus, the required measure of the angle ∠MON is given as 87°.

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The HR manager is using a stratified random sample, which is a technique of dividing the population into multiple strata (groups) and then randomly selecting from each stratum.

The HR manager is using a stratified random sample, which is a technique of dividing the population into multiple strata (groups) and then randomly selecting from each stratum. In this case, the population is divided into two strata, new employees (30%) and experienced employees (70%). The HR manager then randomly selects 17 new employees and 41 experienced employees. This technique ensures that each stratum is represented in the sample, making it more representative of the population. Furthermore, it increases the precision of the sample by focusing on the subgroups that may have different characteristics and opinions on the matter, rather than relying on a simple random sample. The advantage of this sampling design is that it allows the HR manager to make more accurate estimates of the population's opinion on the change in promotion policies.

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The standard deviation is 19.21 while the mean is 20.785.

a) Because E(Y) = 12, var(Y) = 9.

then, for 2Y+20

E(2Y+20)=2E(Y)+20=24+20=44

Var(2Y+20)=4(9)=36.

The average deviation is six.

b)E(X) = 80 var(X) = 144

so, for 3X

E(3X)=3(80)=240

Var(3X)=9Var(X)=9(144)=1296

The average deviation is 36.

c)0.25x+y

E(0.25x+y)=0.25E(x)+E(y)=0.25(80)+12=32

Var(0.25x+y)=0.0625 var(x)+var(y) +2(0.25)Cov(x,y)

Cov(x,y)=0 since x and y are independent.

Var(0.25x+y)=18

Standard deviation = 4.24 d) x – 5 y

E(x-5y)=E(x)-5E(y)=80-5(12)=20

Var(x-5y)=var(x)+25var(y)-2(5)Cov(x,y)

Because X and Y are unrelated, Cov(x,y) = 0

Var(x-5y)=369

The standard deviation is 19.21, while the mean is 20.785

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The total cost of the materials used to construct the wheel is $51.57

The total cost of the materials used to construct the wheel is the sum of the total cost of the wood and the rubber.

Total cost = total cost of the wood + total cost of the rubber

Total cost of the wood = (area of the wood used x cost per square foot) + (circumference of the wheel x cost of the rubber)

Area of the wood = πr²

Where :

π = pi = 3.14

R = radius

3.14 x 1.5² = 7.065 ft²

Total cost of the wood = $17.66

Circumference of the wood = 2πr

2 x 3.14 x 1.5 = 9.42 feet

Total cost of the rubber = 9.42 x 3.60 = $33.91

Total cost of the materials = $33.91 + $17.66 = $51.57

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The value of a in the circle is 6.

Using circle theorem, angles on the circumference from opposite end of a diameter are 90 degrees.

Therefore, the value of angle L is 90 degrees.

Recall the diameter of the circle is MK.

Hence, let's find the value of a as follows:

15a = 90

divide both sides of the equation by 15

15a / 15 = 90 / 15

a = 6

Therefore, the value of a is 6

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The number of batches of muffins she can make will be 5.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other features.

Clayton picks two times as many raspberries and 11/4 cups of blackberries at a berry farm. He brings the berries home and makes mixed-berry muffins with them.

The number of the batches of muffins can be calculated as:-

Number = ( 1¹/₄ + 2 x 1 ¹/₄ ) / ( 3 / 4 )

Number = [  ( 5 / 4 ) + ( 5 / 2 ) ] / ( 3 / 4 )

Number = [ ( 15 / 4 ) / ( 3 / 4 ) ]

Number = 5

Therefore, the number of batches of muffins will be 5.

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Yes, By SAS congruency criteria both ΔDEF and ΔHIG are congruent.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In the given figure,

⇒ DE = IH

⇒ EG = FI

⇒ ∠E = ∠I

Now, In ΔDEF and ΔHIG;

⇒ DE = IH   (Given)

⇒ ∠E = ∠I    (Given)

Since, EG = FI

Hence, We get;

⇒ GF + FI = FG + EG

⇒ GI = FE

So, In ΔDEF and ΔHIG;

⇒ EF = GI   (Common side)

Thus, By SAS congruency criteria both ΔDEF and ΔHIG are congruent.

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The equation below that does not show equivalent expressions when y = 2, is  5y + 25  = 5 ( y + 4 ).

option C.

The equation below that does not show equivalent expressions when y = 2, is determined by solving for y in all the given equation.

y + 4y  = y ( 1 + 4 )

y + 4y = y + 4y

5y = 5y

y = y

y + y + y = 3y

3y = 3y

y = y

5y + 25  = 5 ( y + 4 )

5y + 25 = 5y + 20

5y + 5 = 5y

5 ( y + 1 ) = 5y

y + 1 = y

2 (y + 2 ) = 2y + 4

2y + 4 = 2y + 4

2y = 2y

y = y

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Answer:

-6, -1

Step-by-step explanation:

midpoint M of the line segment

M = (x1 + x2) / 2 , (y1 + y2) / 2

   =  (-5-7) / 2, (5-7) / 2

   =  -12 / 2, -2 / 2

   =  -6 , -1

Answer:0.3

Step-by-step explanation:

Therefore , the solution of the given problem of rectangle comes out to be  A= b* √6²-b².

In the Euclidean plane, a rectangle is merely a cube with four right angles. It is sometimes referred to as an equiangular quadrilateral or a quadrant that seems to have equal angles. The parallelogram also has the option of a straight angle. Four of a square's sides are all the same length. Rectangular quadrilaterals have four equal sides and four 90° vertices. It is sometimes referred as an "equirectangular square" as a result. A rectangle is also referred to as a parallelogram due to the identical and parallel lengths of its opposite sides.

Here,

radio= 3 cm

Al estar un rectángulo inscrito en un círculo, el diámetro del círculo corresponderá a la diagonal del rectángulo

Siendo b la base del rectángulo y a la altura, se tiene que:

6²= a²+b²

a²= √6²-b²

Nota: Se empleó el teorema de Pitágoras

El área del rectángulo está dado por:

A= base* altura

A= b*a

Reemplazando a:

A= b* √6²-b²

Therefore , the solution of the given problem of rectangle comes out to be  A= b* √6²-b².

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The measure of the angle ∠FEB will be 70°.

An infinitely long row of evenly spaced dots that extends in both directions makes up a line. Its length is the only dimension it has. An illustration of a line is a horizontal mark made on a piece of paper. A figure made by two rays that intersect at the same endpoint is referred to as an angle.\

Given that the angle ∠EFB is 35° and BD is the angle bisector of ∠EFD. The measure of the angle ∠FEB will be;-

∠FEB = 2 x ∠EFB

∠FEB = 2 x 35

∠FEB  = 70°

Therefore, the value of the angle ∠FEB will be 70°.

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The solution is Marginal cost is  (1200 - 1000) / (30 - 20) = 12.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

In order to calculate marginal cost, producers must compare the difference of producing one unit to the cost of producing the next unit

Marginal cost is the change in total cost as a result of increasing output produced by one unit.  

For example, if the total cost of producing 20 units of a good is 1000 and the total cost of producing 30units is 1200.

Marginal cost is  (1200 - 1000) / (30 - 20) = 12

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Junita prefers Samsung Television brand with score of 7.6. A multi-attribute model is a way of evaluating products or services based on multiple attributes or characteristics.

In this scenario, Juanita is evaluating four television brands based on four criteria: price, quality, screen size, and features. She assigns a weight to each criteria, indicating its importance to her, with price having 20% importance, quality having 30% importance, screen size having 30% importance, and features having 20% importance. She then rates each brand on each criteria and calculates an overall score for each brand using the weights and ratings. Based on her evaluations, Juanita prefers the Samsung brand as it has the highest overall score.

Based on the multi-attribute model, Juanita prefers the Samsung television brand. Here's the calculation:

Samsung:  [tex]5 *0.20 + 8 * 0.30 + 8 *0.30 + 9 * 0.20 = 1 + 2.4 + 2.4 + 1.8 = 7.6[/tex]

Sony:  [tex]4 * 0.20 + 8 * 0.30 + 8 * 0.30 + 9 * 0.20 = 0.8 + 2.4 + 2.4 + 1.8 = 7.4[/tex]

LG: [tex]8 *0.20 + 6 *0.30 + 6 * 0.30 + 5 * 0.20 = 1.6 + 1.8 + 1.8 + 1 = 6.2[/tex]

Vizio:  [tex]9 * 0.20 + 5 * 0.30 + 4 * 0.30 + 4 * 0.20 = 1.8 + 1.5 + 1.2 + 0.8 = 5.3[/tex]

Juanita prefers the Samsung television brand with a score of 7.6 compared to the other brands.

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there is no difference in the values of Time for Idil or Sophie in that their amount will be tripled.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Idil invested $150 in an account paying an interest rate of 5.785% compounded annually. Sophie invested $150 in an account paying an interest rate of 5.625% compounded continuously.

From the general formula of compound interest:

Final value A = (1 + r/n)^nt,

where P is the principal balance

r is the interest rate

n is the number of times interest is compounded annually

t is the number of years,

For Idil,

P = 150, r = 5.782, A = 3*p = 450, and n = 1

Thus,

450 = 150 (1 + 5.785%)^t

3 = (1.05785)^t

t = 19.535 years

The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.785% per year and compounded 1 time per year is 19.535 years.

(about 19 years 6 months)

For Sophie,

P = 150, r = 5.625, A = 3*p = 450

First, convert R as a percent to r as a decimal

r = R/100

r = 5.625/100

r = 0.05625 per year,

Then, solve the equation for t

t = ln(A/P) / r

t = ln(450.00/150.00) / 0.05625

t = 19.531 years

The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.625% per year and compounded continuously is 19.531 years.

(about 19 years 6 months)

therefore, there is no difference in the values of Time for Idil or Sophie.

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Answer:$69.08

Step-by-step explanation:

His average speed in blocks per hour is 18.66 blocks per hour

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

It took Lex from 10:00 a.m. to 11:45 a.m. to walk 14 blocks

This means that

Blocks = 14

Time = 45 minutes = 3/4 hour

The speed is then calculated as

Speed = 14/(3/4)

Evaluate

Speed = 18.66

Hence, the speed is 18.66 blocks per hour

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The relationship between M and C can be given by the equation C= 6M + 12

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month.

Now M represents the number of movies and C represents the user's total charge for the month

Thus C= 6M + 12

where 6M is the total cost due to renting some number of movies M

Hence, The relationship between M and C can be given by the equation C= 6M + 12

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Answer: $25,000

Step-by-step explanation:

You invest $10,000 annually. If you divide 10,000 by 4, you get 25,000. It's $25,000 quarterly.

The number 9,839,038 after indicated rounding off gives the number 9,839,000.

Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.

Rounding can be done for whole numbers as well as decimals.

Given is a whole number 9,839,038.

We have to round it to the place shown where the digit is 9.

Look at the next digit right to 9.

It is 0, which is less than 5.

So replace all the digits next to 9 by 0.

We get the number 9,839,000.

Hence the rounded number is 9,839,000.

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The value of the limit that exists at the given numbers is approximately 0.5.

First of all at x = 3.1, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 3.1} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]\frac{(3.1)^2-3(3.1)}{(3.1)^2-9}[/tex] = [tex]\frac{0.31}{0.61}[/tex] ≅ 0.508197

At x = 3.05, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 3.05} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex]  =  [tex]$\frac{(3.05)^2-3(3.05)}{(3.05)^2-9}=\frac{0.1525}{0.3025}$[/tex] ≅  0.504132

At x = 3.01, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 3.01} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex]  = [tex]$\frac{(3.01)^2-3(3.01)}{(3.01)^2-9}=\frac{0.0301}{0.0601}$[/tex] ≅  0.500832

At x =  3.001, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 3.001} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] =  [tex]$\frac{(3.001)^2-3(3.001)}{(3.001)^2-9} $[/tex]=  [tex]$\frac{3.001 \times 10^{-3}}{6.001 \times 10^{-3}}$[/tex] ≅0.500083

At x =  3.0001, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 3.0001} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.0001)^2-3(3.0001)}{(3.0001)^2-9} $[/tex]=  [tex]$\frac{3.001 \times 10^{-4}}{6.001 \times 10^{-4}}$[/tex] ≅ 0.500008

At x = 2.9, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 2.9} \frac{x^2-3 x}{x^2-9} $$[/tex]  = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] =  [tex]$\frac{(2.9)^2-3(2.9)}{(2.9)^2-9} $[/tex]=  [tex]$\frac{-0.29}{-0.59}$[/tex] = 0.491525

At x = 2.95, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 2.95} \frac{x^2-3 x}{x^2-9} $$[/tex]  = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] =  [tex]$\frac{(2.95)^2-3(2.95)}{(2.95)^2-9} $[/tex]=  [tex]$\frac{-0.1475}{-0.2975}$[/tex] = 0.495798

At x = 2.99, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 2.99} \frac{x^2-3 x}{x^2-9} $$[/tex]  = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] =  [tex]$\frac{(2.99)^2-3(2.99)}{(2.99)^2-9} $[/tex]=  [tex]$\frac{-0.0299}{-0.0599}$[/tex] = 0.499165

At x = 2.999, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 2.999} \frac{x^2-3 x}{x^2-9} $$[/tex]  = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] =  [tex]$\frac{(2.999)^2-3(2.999)}{(2.999)^2-9} $[/tex]=  [tex]$\frac{-2.999 \times 10^{-3}}{-5.999 \times 10^{-3}}$[/tex] = 0.499917

At x = 2.9999, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be

[tex]$$\lim _{x \rightarrow 2.9999} \frac{x^2-3 x}{x^2-9} $$[/tex]  = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] =  [tex]$\frac{(2.9999)^2-3(2.9999)}{(2.9999)^2-9} $[/tex]=  [tex]$\frac{-2.999 \times 10^{-4}}{-5.999 \times 10^{-4}}$[/tex] = 0.499992

From above all, we can see that the limit is approximately equal to and tends towards 0.5. So 0.5 will be our answer.

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Your question was incomplete, your most probable question was:
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).

[tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9}[/tex],  x = 3.1, 3.05, 3.01, 3.001, 3.0001, 2.9, 2.95, 2.99, 2.999, 2.9999

The solutions to the equation are x = -4 and x = 4

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

f(x)=−|x−2|+2 and g(x)=1/2x−2.

next, we graph the functions in the same coordinate plane

See attachment for the graph

The point of intersections represent the solutions

These points are x = -4 and x = 4

Hence, the solutions are x = -4 and x = 4

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The nature of the disaster and the factors that contributed to the survival of the passengers.

The formula used to calculate the survival rate of the passengers on the Titanic is as follows:

Number of Surviving Passengers/Total Number of Passengers * 100

For example, if there were 500 passengers on the Titanic and 100 of them survived, then the survival rate would be calculated as follows:

100/500 * 100 = 20%

This formula is useful for determining the survival rate of passengers on the Titanic, as well as any other disaster. By understanding the survival rate of the Titanic, we can better understand the nature of the disaster and the factors that contributed to the survival of the passengers.

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Complete question: What was the survival rate of passengers on the Titanic?

Step-by-step explanation:

Since force doesn't depend on mass and varies directly, you can set up a proportion. group the F's together and the acceleration together, as so

[tex] \frac{20}{16} = \frac{5}{x} [/tex]

Next, cross m multiply

[tex]20x = (16)(5)[/tex]

[tex]20x = 80[/tex]

Lastly, divide by 20

[tex]x = 4m {s}^{2} [/tex]

The acceleration of the object when force is 16N is 4m/s².

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The force acting on the object varies directly with the object's acceleration.

Therefore, F ∝ a.

F = ka.

20 = 5k.

k = 4.

Now,

16 = 4a.

a = 4.

So, The acceleration is 4m/s²

learn more about proportion here :

https://brainly.com/question/7096655

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