You are taking a multiple - choice quiz that consists of five questions. Each question has four possible answers, only one of which is correct. To complete the quiz, you randomly guess the answer to each question. Find the probability of guessing (a) exactly three answers correctly, (b) at least three answers correctly, and (c) less than three answers correctly.

If the population grew to 35203 by the year 2019 , then the equation to model this situation is y = 1174x + 29333 .

We use the given data points to create a linear equation to model the population growth over the years.

Let , x₁ = 0 represents the year 2014

⇒ y₁ = 29333 represents the population in the year 2014

⇒ x₂ = 5 represents the year 2019

⇒ y₂ = 35203 represents the population in the year 2019

Using these variables, we can find the slope of the line that represents the population growth:

So , slope = (y₂ - y₁)/(x₂ - x₁)

⇒ slope = (35203 - 29333)/(5 - 0)   ;

⇒ slope = 5870/5 = 1174  ;

Now , by using the point-slope form of a linear equation

we get ;

⇒ y - y₁ = m(x - x₁)  ;

⇒ y - 29333 = 1174(x - 0)  ;

Simplifying this equation ;

we get ;

⇒ y = 1174x + 29333 ;

Therefore, the equation for the model is y = 1174x + 29333, where y represents the population and x represents the number of years since 2014.

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The given question is incomplete , the complete question is

The population in a small us city has been increasing linearly. in 2014, the population of this town was 29333. and by the year 2019, it grew to 35,203. Find the equation for this model ?

The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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Answer:

Ext angles = 40 degs 360/40 = 9 sides

Step-by-step explanation:

Answer:

It mostly depends on the question

Step-by-step explanation:

The prove is as follows

Statement             Reason

line BC || line DA  Definition of parallelogram

Draw line AC        Unique line postulate

AC = CA                Reflexive property (common sides)

∠BAC = ∠DCA      Alternate interior angles

∠BCA = ∠DAC      Alternate interior angles

Δ ABC ≅ Δ CDA   ASA triangle postulate

AB ≅ CD               CPCTC theorem

BC ≅ DA               CPCTC theorem

The ASA (Angle-Side-Angle) postulate is a statement about the relationship between the angles and sides of triangles. It states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. In other words, if two triangles have the same shape and size, then they are congruent.

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." This theorem states that if two triangles are congruent, then all their corresponding parts are congruent. In other words, if two triangles have the same shape and size, then all their angles and sides are congruent.

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When working with fractional readings, it is often necessary to convert them to a different format to ensure consistency and compatibility. One common conversion is to express the fractions as decimals or percentages.

This allows for easier comparison and calculation.

For example, if you have a fractional reading of 3/4, you can convert it to 0.75 or 75%. By converting the fraction, you bring the measurement into a standardized range, making it easier to work with and understand.

Converting fractions to decimals or percentages is a useful practice in various fields, including mathematics, engineering, and statistics, ensuring uniformity and facilitating data analysis.

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Answer:

1/12

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

1 x 1 = 1

3 x 4 = 12

Answer: Yes you can use the HL theorem

Explanation:

HL = hypotenuse leg

The tickmarks tell us about the congruent hypotenuse sides. This takes care of the "H" from "HL".

The "L" portion is because BC = BC (reflexive property) which are the congruent legs.

So we have enough info to use the HL theorem to prove the triangles are congruent.

Note: The HL theorem only works for right triangles.

If the yearly cost for the dental claims are normally distributed , then the yearly cost at which 35% of the employee fall at or below is $91.35  .

In the question ,

it is given that ,

the yearly cost for the dental claims are normally distributed ;

and the mean (μ) is 105 , standard deviation(σ) is 35 .

we know that the z value that corresponds to 35th percentile from standard normal table is : z = -0.385  ;

let the yearly cost be "x" ;

the yearly cost can be calculated using the formula ;

x = z×(σ) + μ

x = (-0.385)×35 + 105

Simplifying further ,

we get ;

x = 91.525

x ≈ 91.53

Therefore , the correct option is (d) 91.53  .

The given question is incomplete , the complete question is

The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of $105 and a standard deviation of $35. what is the yearly cost at which 35% of the employees fall at or below is ?

(a) $118.48

(b) $127.29

(c) $82.71

(d) $91.53

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The number of infections in week 7 will be 45.

To find what will the number of infections be in week 7:

Therefore, the number of infections in week 7 will be 45.

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Answer:

x = 3

Step-by-step explanation:

Factor using difference of cubes and set each factor equal to 0.

Answer:

x = 3

explanation:

Correct

∬D curl F · dA = ∬D (Qx - Py) dA= ∫02π ∫0^2 (2y - xy2) r dr dθ= 8π/3, by using polar coordinates.

To evaluate the line integral of f(x, y) = xy2î + 2yxſ over C,

where C is bounded by y = x, x2 + y2 = 8 and y = 0 in the positive rotation,

let's start by sketching the region D and showing it:

Green's Theorem states that the line integral of a vector field F around a closed curve C is equal to the double integral over the region D bounded by C of the curl of F.

Mathematically,

Green's Theorem

∫CF·dr = ∬D curl F · dA

where, C is a closed curve in a plane and D is the region in the plane bounded by C,

F is a vector field whose components have continuous partial derivatives on an open region in R2 that contains D and curl F is the curl of F.

The line integral of the given vector field F along C is

∫CF · dr = ∫C Pdx + Qdy

where P = xy2, Q = 2yx, and dr = dxî + dyſ

The boundary of the region D is the given curve C.

So the integral can be evaluated by using Green’s theorem.

∬D curl F · dA = ∬D (Qx - Py) dA

Here, curl F = Qx - Py

By computing the partial derivatives of P and Q, we can get ∂P/∂y = 2xy and ∂Q/∂x = 2y

Thus,∬D curl F · dA = ∬D (Qx - Py) dA= ∫02π ∫0^2 (2y - xy2) r dr dθ= 8π/3, by using polar coordinates..

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Answer:

160cm

Volume of trapezium part=( 1/2 × (2+5) ×2) ×10=70

Volume of rectangular part= 3×5×10=150

Volume of one chocolate bar = 70 +150=220

Total volume of chocolate needed for 1300 bars of chocolate= 220×1300=286000

1.5m =150 cm

Radius=150÷2=75

Volume of clinder=πR2H= π75×75×height

Height=286000÷5625π=159.732533=160( to 3s.f)

By using the concept of Compound interest, Number of payment periods in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = 12

What is Compound interest?

The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

This problem can be solved by using the concept of compound interest

Number of  payment periods are in a 6-year, 8% bond with an effective interest rate of 6%, and paid semiannually = \(6 \times 2 = 12\)

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On solving the provided question by slope intercept form, equation formed id=s 3x + 4y - 14= 0 .

One of the most popular ways to express a line's equation is in the slope intercept form of a straight line. Given the slope of the straight line and the y-intercept, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). A line's equation is the equation that each point on the line fulfills. There are several ways to solve the equation for a straight line given as, - Slope-intercept form, Point slope form Two-point form and Intercept the form

slope = -3/4

points ( -2,5 )

equation,

(y - y1) = m(x - x1)

( y - 5) = -3/4(x+2)

4y - 20 = -3x - -6

3x + 4y - 14= 0

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Answer:

.01

Step-by-step explanation:

160/1000= .16

150/1000= .15

so the difference is .01

The best summarizes for the result is:

O There is a moderate negative correlation between the variables.

A correlation coefficient measures the strength and direction of the relationship between two variables. The coefficient ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

In this case, the correlation coefficient of -0.524 indicates a moderate negative correlation between the variables. This means that as the value of one variable increases, the value of the other variable decreases, and vice versa. The negative sign indicates that the relationship is negative, and the absolute value of the coefficient (0.524) indicates that the relationship is moderate in strength.

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Answer:

Step-by-step explanation:

$587.34 x 6.2% = $36.42

$587.34 x 1.45% = $8.52

$36.42 + $8.53 + $164.45 + $76.34 + $50 + $8 + $23 + $8 = $374.73

$587.34 - $374.73 = $212.61

Michael's net pay for this pay period should be $212.63.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's calculate Michael's total deductions first:

Social Security tax = 6.2% of $587.34 = $36.40

Medicare tax = 1.45% of $587.34 = $8.52

Federal withholding tax = $164.45

State withholding tax = $76.34

Retirement insurance contribution = $50.00

Disability insurance fee = $8.00

Medical insurance fee = $23.00

Dental insurance fee = $8.00

Total deductions.

= $36.40 + $8.52 + $164.45 + $76.34 + $50.00 + $8.00 + $23.00 + $8.00

Total deductions = $374.71

Now we can calculate Michael's net pay:

Net pay = Gross pay - Total deductions

Net pay = $587.34 - $374.71

Net pay = $212.63

Therefore,

Michael's net pay for this pay period should be $212.63.

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The value of x is 7

To determine the value, we have that;

m<BC = 2 < BDC

Then, we have;

<BDC = 1/2(2x + 16)

<BDC = x + 8

Also, we have that;

m<ED = 2 < ECD

m<ECD = 1/2 (7x - 9) = 3.5x - 4.5

Bute, we have that;

<<BDC + <ECD + < DAC = 180; sum of angles in a triangle

substitute the values

x + 8 + 3.5x - 4.5 + 145 = 180

collect the like terms

4.5x = 31.5

Divide both sides by 4.5

x = 7

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Answer:

x = 3/2   y = 7

Step-by-step explanation:

We can subtract each side of equation 1 from each side of equation2 which gives us:

(2x + 4y) - (2x + y) = 31 - 10

3y = 21

y = 7

Substitute this value into one of the equations to find x:

2x + y = 10     (substitute 7 for y)

2x + (7) = 10     (subtract both sides by 7)

2x = 3    (divide both sides by 2)

x = 3/2

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Answer:

C

Step-by-step explanation:

The set of all 3 x 3 nonsingular matrices with the standard operations is a vector space. A set is a vector space when it satisfies the eight axioms of vector spaces. The eight axioms that a set has to fulfill to be considered a vector space are:A set of elements called vectors in which two operations are defined.

Vector addition and scalar multiplication. Axiom 1: Closure under vector addition Axiom 2: Commutative law of vector addition Axiom 3: Associative law of vector addition Axiom 4: Existence of an additive identity element Axiom 5: Existence of an additive inverse element Axiom 6: Closure under scalar multiplication Axiom 7: Closure under field multiplication Axiom 8: Distributive law of scalar multiplication over vector addition The given set of 3 x 3 nonsingular matrices satisfies all the eight axioms of vector space operations, so the given set is a vector space.

The given set of all 3 x 3 nonsingular matrices with the standard operations is a vector space as it satisfies all the eight axioms of vector space operations, so the given set is a vector space.

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the integral of the line, where c is the specified curve. The line integral is (x 9y) dx x2 dy, where C is the provided curve. The line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0), respectively, make up the integral c (x+2y)dx+x2dy, C. is 95/3

\(\int\limits^a_c {(x+9y,x^{2} )} \, dr_{2} = \int\limits^1_0{9+t+9-9t, (9+t )^2} .(1, -1)\, dt\)

it is possible to parameterize the first line segment by

\(r_{1} (t) = (0,0)(1-t) + (9,1)t = (9t,t)\) with 0 ≤ t ≤ 1 indicate this first section with \(C_{1}\) then

\(\int\limits^a_c {(x}+9y,x^2 ) \, dr_{1} = \int\limits^1_0 {(9t+9t,81t^2) . (9,1)} \, dt\\ \\= \int\limits^1_0 {(162t + 81t^2) } \, dt\\\\= 108\)

secondly the line segment \(C_{2}\) can be characterised as

\(r_{2} (t) = (9,1)(1-t) + (10,0)t = (9+t,1-t)\) again using interval  0 ≤ t ≤ 1  then

\(\int\limits^a_c {(x+9y,x^{2} )} \, dr_{2} = \int\limits^1_0{9+t+9-9t, (9+t )^2} .(1, -1)\, dt\)

= -229/3

finally ,

= 108-229/3

= 95/3

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The three values that you need to know in order to perform a z-score are the mean, the standard deviation, and the raw score.

The mean is the average of the data set, the standard deviation measures the spread of the data, and the raw score is the individual data point that you are comparing to the rest of the data set. The z-score formula is:

z = (x - μ) / σ

Where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation. By knowing these three values, you can calculate the z-score and determine how many standard deviations away from the mean the raw score is.

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We can tell if a character is direct or Indirect  by the five methods which are action, reactions, physical description,  inner thoughts,  and speech.

The Characterization in literature is the process that the authors use to develop characters and create images of characters for audience.

There are two different approaches for characterization, which are Direct Characterization and Indirect Characterization.

The methods by which we can know that a character is Direct or Indirect are :

(i) Physical description - In this the character's physical appearance is described. For example, How the character dresses might reveal something about the character.

(ii) Action - Is the character a good person or a bad person can be told by his Action .

(iii) Inner thoughts - The inner thoughts of character reveals the personality .

(iv) Reactions - The Effect on other characters also reveals about the personality of character .

(v) Speech - What character says provides a great insight for the reader.

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Its 10.4 you are correct

The probability that the other child is also a girl, given that one of them is a girl, is 2/3 or approximately 0.6667.

To determine the probability that the other child is also a girl given that one of them is a girl, we need to consider the possibilities of the gender combinations for Alice's two children.

Let's denote the gender of the first child as G (girl) and B (boy), and the gender of the second child as G' and B'.

There are four possible combinations for the gender of the two children: GG, GB, BG, and BB.

However, we are given that one of the children is a girl. This eliminates the BB combination since we know both children cannot be boys.

Thus, we are left with three possible combinations: GG, GB, and BG.

Out of these three combinations, two of them involve at least one girl: GG and GB. This means there is a 2 out of 3 chance that the other child is a girl.

Therefore, the probability that the other child is also a girl, given that one of them is a girl, is 2/3 or approximately 0.6667.

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By applying the z-score concept, it can be concluded that the manufacturer should announce a guaranteed mileage of 44528 miles.

z-score is the standard value or the amount of deviation of a value from the mean.

z = (x - μ) / σ   where:

x = the observed value

μ = the mean

σ = the standard deviation

From the problem we get:

μ = 47,900 miles

σ = 2,050 miles

No more than 5% of the tires will have to be replaced, P(X) = 0.05.

So it is X when Z = -1.645.

Now we want to find the x:

             z = (x - μ) / σ

    -1.645 = (x - 47900) / 2050

-3372.25 = x - 47900

            x = 47900 - 3372.25

               = 44527.75

               ≈ 44528 miles

Thus the manufacturer should announce a guaranteed mileage of 44528 miles.

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Answer:

See below

Step-by-step explanation:

A roll of ' 1 ' or  ' 4 '    would be a perfect square ....two chances out of a possible six rolls    1/3 chance