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Answer:

(A) 30 pages

Step-by-step explanation:

Let x = total number of pages in the book.

She read half the book in Monday. She read x/2.

She read 90 pages on Tuesday. By now she read a total of x/2 + 90.

She has 1/8 left to go. That means she read 7/8 of the book.

7/8 x = x/2 + 90

Multiply both sides by 8.

8 × 7/8 x = 8 × x/2 + 8 × 90

7x = 4x + 720

3x = 720

x = 240

The book is 240 pages long.

She has 1/8 to go.

1/8 × 240 = 30

Answer: (A) 30 pages

The demand is positive for t greater than 3. The correct answer is option (a).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

Given that,

The demand function for cell phone is given as,

C(t) = -√t^2 + 4t - 12 + 3

Which can be written in simple terms as,

C(t) = -t + 4t - 12 + 3

       = 3t - 9

For positive demand C(t) ≥ 0

=> 3t - 9 ≥ 0

=> t ≥ 3

Which is valid for option (a) only.

Hence, the demand is positive for t ≥ 3.

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Hi! The answer would be (6,3)

Have a good day!

The equation the given statement is y=ax.

What is equation?

  The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. Equations come in two varieties: identities and conditional . All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Here the weight of the steel beam is proportional to length.

let y be weight and x be length of it. Then

=> y ∝ x

=> y=ax

where a is the constant

we can find it if we have two sets of values of y and x.

Therefore the equation the given is y=ax.

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a) The slope is infinity.

b) We can't write the linear equation in the slope-intercept form because the slope is infinity, in this case, the line is written as x = 2.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

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

Here we have two points (2, 1) and (2, 0), then the slope is:

slope = (1 - 0)/(2 - 2) = 1/0 → ∞

So the slope is infinity, as the case for all vertical lines.

b) Why we can't write the linear equation in the traditional form?

This happens because the slope is infinity, the vertical linear equations are written as:

x = a

In this case, we can see that the line is at x = 2, so that is our linear equation.

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Answer:

a) Total preferred dividend = $37,020; total common stock dividend = $26,980.

b) Total preferred dividend = $12,340; total common stock dividend = $51,660.

C) see explanation section.

Explanation:

Requirement - A

If the preferred dividend is cumulative.

Common stock = $12 x 50,000 = $600,000

Preferred stock = $19.5 x 7,910 = $154,245

Given,

Retained Earnings = $240,000, and Dividend = $64,000.

Generally, cash dividend is distributed to the preferred and common stockholders. However, after paying the preferred stock, dividend is paid to the common stockholders.

Therefore, preferred dividend = $154,245 x 8% = $12,340 for 2019.

As the preferred dividend is cumulative, the preferred stockholders will get the dividend for 2017 and 2018 if there remains any extra dividend after giving for 2019.

For 2017 = $12,340

For 2018 = $12,340

For 2019 = $12,340

Total preferred dividend = $37,020.

Therefore, the total common stock dividend = $(64,000 - 37,020) = $26,980.

Requirement - B

If the preferred dividend is non-cumulative.

Therefore, preferred dividend = $154,245 x 8% = $12,340 for 2019.

As the preferred dividend is non-cumulative, the preferred stockholders will not get the dividend for 2017 and 2018 despite remaining extra dividend after providing for 2019.

Therefore, preferred dividend = $12,340

Common stock dividend = $(64,000 - 12,340) = $51,660.

Requirement - C

The common stock dividend is more in non-cumulative as the company does not pay the previous years' dividends to the preferred dividend. On the other hand, if the company pays the dividend for the last years', which is known as cumulative, the dividend will become less. Therefore, the common stockholders will get fewer dividends because of paying the previous years' dividend to the preferred stockholders.

The factors would cause a more favorable dividend for the common stockholders if preferred dividends were non-cumulative, not in arrears, and there is an increase of distribution of dividends.

Answer:

383.7

Step-by-step explanation:

Draw the picture.

You have a right triangle with height = 107 and base = 131

-----

angle = tan^-1(107/131) = 39.24 degrees

==============================

The two samples produce different confidence intervals because they have different standard deviation values.

Confidence interval for Population A

The confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From the given data, we have

Xbar = 4.5

S = 3.741657387

n = 8

df = n – 1 = 7

Confidence level = 95%

Critical t value = 2.3646

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 4.5 ± 2.3646*3.741657387/sqrt(8)

Confidence interval = 4.5 ± 3.1281

Lower limit = 4.5 - 3.1281 = 1.3719

Upper limit = 4.5 + 3.1281 = 7.6281

Confidence interval = (1.3719, 7.6281)

Confidence interval for Population B

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 4.5

S = 2.449489743

n = 8

df = n – 1 = 7

Confidence level = 95%

Critical t value = 2.3646

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 4.5 ± 2.3646*2.449489743/sqrt(8)

Confidence interval = 4.5 ± 2.0478

Lower limit = 4.5 - 2.0478 = 2.4522

Upper limit = 4.5 + 2.0478 = 6.5478

Confidence interval = (2.4522, 6.5478)

The above two samples produce different confidence intervals even though they have the same mean and range because they have different standard deviation values.

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The solution for x in the given logarithmic equation, log₁₆x = -1/2, is x = 1/4

From the question, we are to solve the given equation for x.

The given equation is

log₁₆x = -1/2

To solve the equation, we will determine the value of x.

Solving the equation

log₁₆x = -1/2

From one of the laws of logarithm,

logₐy = n ⇒ y = aⁿ

Thus,

The equation becomes

x = 16^(-1/2)

By applying one of the laws of indices, we get

x = (√16)⁻¹

x = 4⁻¹

x = 1/4

Hence, the value of x is x =1/4

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Only 46 students like vanilla ice cream.

What is union and interaction?

Union of Disjoint Sets:

If A and B are two finite sets and if A ∩ B = ∅, then

n(A ∪ B) = n(A) + n(B)

In simple words if A and B are finite sets and these sets are disjoint then the cardinal number of Union of sets A and B is equal to the sum of the cardinal number of set A and set B.

Given,

total number of students = 97

students who like chocolate and vanilla flavors = 25

students who like strawberry and vanilla flavors  = 16

students who like chocolate and strawberry flavors = 17

students who like all three flavors = 9

students who do not like ice cream = 5

Let C,S,V represent the chocolate, strawberry, vanila

therefore,

n(C∪S∪V) = n(C) + n(S) + n(V) - n(C∩V) - n(V∩S) - n(C∩S) + n(C∩V∩S)

97 = n(C)+n(S)+n(S)-25-27-9-5

141 = n(C) +2n(S)

141 = 3n(C)

n(C)=48

n(S) = n(V) =n(C)-2

=46

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Answer:

4pm

10:37 + 4:45 hours +38 min makes arrival time 4pm

The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Quantity of electricity used in kilowatts is;

1000 watts = 1 kilowatts

2,500 watts = 2.5 kilowatts

Given that Number of hours Val runs AC per day = 5 hours

Number of days = 30 days

Cost of electricity = $0.18 kilowatts per hour

The Cost of Val’s AC to run for a summer month of 30 days can be calculated as;

= Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity

= 2.5 × 5 × 30 × 0.18

= $67.5

The total cost to run Val’s AC costs for a summer month of 30 days will be $67.5.

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Answer:  9.22

Step-by-step explanation:

distance in x direction:  ║-4║ + 2 = 6

distance in y direction:  5 + ║-2║ = 7

Use pythagorean theorem to find hypotenuse of triangle with legs of 6 and 7:

[tex]d^{2} = 6^{2} + 7^{2} = 85\\d = \sqrt{85} = 9.2195 = 9.22[/tex]

The Mean measure should be used to summarize the data in all three problems.

What is the mean?

In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific group of data, often in order to better understand the overall value of a data set.

Generally,

For ratio and interval type of data, we use mean as the central tendency

For the ordinal type of data, we use the median as the central tendency

and For the nominal type of data mode is prefered.

Interval data:- In this type of data point lies in some interval on a scale.

Like temperature in degrees Fahrenheit, it has some range of value on the measurement scale of temperature.

Ratio Data:- It is similar to interval type of data but absolute zero is treated as the point of origin.No negative value

Example:- temperature in kelvin (0 is the origin)

Ordinal data:- It is of categorical type of data that is in the natural order and the distance between the two data is not known.

Example:- How you describe your last purchasing experiences,

1) Very Pleasant 2) Somewhat Pleasant 3) Neutral 4) Somewhat Unpleasant 5) Very Unpleasant.

Nominal data:- In this data is leveled or named without any quantitative value.

Example:- Colour of hair, gender, country, etc.

a)

In part (a) the data is ratio type.

Hence, the Mean is the best central tendency of measurement.

b)

In (b) part also ratio type of data.

Hence, the Mean is the best central tendency of measurement.

C)

In this part, data is of the Interval data.

Hence, the Mean is the best central tendency of measurement.

Therefore, the Mean measure should be used to summarize the data in all three problems.

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The fraction of the given is 1/7 .

What is fraction?

 A fraction that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Here let us take x as numerator and y as denominator. Then

If the numerator is multiplied by 3 and denominator is reduced by 2, we get 3/5 ,

=> 3x/y-2 = 3/5

=> 5*3x =3(y-2)

=> 15x=3y-6

=> 5x=y-2

=> y =5x+2------>1

Now if the numerator is increase by 4 and the denominator is double we get 5/14,

=> (x+4)/2y = 5/14

=> 14x+56 = 10y

=> 7x+28=5y ---->2

Here put 1 into 2 then,

=> 7x+28 = 5(5x+2)

=> 7x+28=25x+10

=>18x=18

=> x =1

Now put x=1 into 1 then,

=> y =5(1)+2 = 7.

Therefore the given fraction is x/ y = 1/7.

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The unknown variable T has a value of T = 2

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

Formula; I = PRT

The above formula is a simple interest formula, where

Values:

I=1920​, P=24,000​, R=0.04

Substitute I=1920​, P=24,000​, R=0.04 in the equation I = PRT

So, we have

1920 = 24000 * 0.04 * T

Evaluate the products

1920 = 960 * T

So, we have

T = 1920/960

Evaluate

T = 2

Hence, the value is 2

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Answer:

x = 148.76

Step-by-step explanation:

tan (37) = 81/x

x = 81/(tan (37)) = measure of "x" from after the height is 81

tan (63) = 81/x

x = 81/(tan (63)) = measurement of "x" from before the height is 81

81/(tan (63)) + 81/(tan (37)) = x

x = 148.76

The value of the double integration is 7776 after solving and integration. the answer is 7776.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

Double integration (x + y) dA

y = x²

y² = 216x

y = √216 √x

∫∫(√216 √x +  x²)

After solving:

[tex]\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy[/tex]

=7776

Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.

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The solution for implicit differentiation is

[tex]\frac{d^{2}y }{dx^{2} } =-\frac{16}{25y^{3} }[/tex]

What is implicit differentiation?

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Let the function be [tex]4x^{2} -5y^{2} =4[/tex]   be equation (1)

Now , on differentiating the terms with respect to y , we get

[tex]4x^{2} -5y^{2} =4[/tex]

[tex]8x-10y\frac{dy}{dx} = 0[/tex]

[tex]8x=10y\frac{dy}{dx}[/tex]

[tex]\frac{dy}{dx}=\frac{4}{5} \frac{x}{y}[/tex]   be equation (2)

So , the first derivative is [tex]\frac{dy}{dx}=\frac{4}{5} \frac{x}{y}[/tex]

Now , on taking the derivative of equation (2) , we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5}(\frac{y-x\frac{dy}{dx} }{y^{2} } )[/tex]

Substituting the value for dy/dx from equation (1) , we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5}(\frac{y-x\frac{4}{5}\frac{x}{y} }{y^{2} } )[/tex]

On simplifying the equation , we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5} ( \frac{5y^{2}-4x^{2} }{5y^{3} } )[/tex]    be equation (3)

Substituting the value for 5y² - 4x² = -4 from equation (1) we get

[tex]\frac{d^{2} y}{dx^{2} } =\frac{4}{5} ( \frac{-4 }{5y^{3} } )[/tex]

So , the implicit differentiation value is

[tex]\frac{d^{2} y}{dx^{2} } =\frac{-16}{25y^{3} }[/tex]

Hence , The solution for implicit differentiation is

[tex]\frac{d^{2}y }{dx^{2} } =-\frac{16}{25y^{3} }[/tex]

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A) The slope is 3/2

B) The line in point-slope form: y = (3/2)*(x - 2) + 10

C) The line in slope-intercept form: y = (3/2)*x  + 7

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

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

Here the line goes through (2, 10) and (-2, 4), then the slope is:

a = (10 - 4)/(2 + 2) = 6/4 = 3/2

b) The line in point-slope form for a point (h, k) is:

y = a*(x - h) + k

So here we get:

y = (3/2)*(x - 2) + 10

c) Expanding the above equation we will get:

y = (3/2)*x - (3/2)*2 + 10

y = (3/2)*x  + 7

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The probability that a student chosen at random is in the choir or band or both is 0.911

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In mathematics terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain.

Total number of students in the school = 450

number of students in choir = 110

number of students in band = 240

number of students in both = 60

Probability a student chosen at random is in the choir or band or both is

110/450 + 60/450 + 240/450

= 410/450 which is 0.911

In conclusion, the probability of a student being in music, or band or both is 0.911

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The perimeter of a triangle is 78 if QA=10. SQ=28, BR=15 and A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ in triangle QRS.

In Euclidean geometry, any three non-collinear points define a unique triangle and, at the same time, a unique plane. In other words, the triangle is contained in just one plane, and every triangle is contained in at least one plane. There is just one plane and all triangles are enclosed in it if the entire geometry is merely the Euclidean plane; however, this is no longer true in higher-dimensional Euclidean spaces. Unless otherwise specified, this article is about triangles in Euclidean geometry, specifically the Euclidean plane.

Given,

In triangle QRS,  A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ

Also given that,

QA=10

BR=15

SQ=28

QA=RA=10

BR=SB=15

Therefore, perimeter of the triangle=RQ+QS+RS

=(RA+QA)+(QS)+(RB+BS)

=(10+10)+(28)+(15+15)

=20+28+30

=78

Hence, the perimeter of a triangle=78

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Answer:

B- function 1, because it’s rate of change is 2

Step-by-step explanation:

the rate of change of function 2 can be found since it is in slope intercept form

y=mx+b and m is slope and in this case m is 1/2

1/2 is function 2 rate of change

To find function 1 rate of change we use y2-y1/x2-1

using (1,2) and (-1,-2)

-2-2/-1-1

-4/-2

2 is the slope of function 1

Function 1 has a greater rate of change so  B is correct

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The dividend with a divisor of 3 that will yeild the quotient 25 with a remainder of 1 is 76.

In division of fractions, we have the divisor which is the denominator, the dividend which is the numerator and then the quotient which is the whole number as the result and sometimes the remainder when the divisor does not divide the dividend exactly.

For us to have a quotient of 25 and a remainder of 1, with the divisor as 3, then the dividend is 76.

Therefore, 76 divided by 3 is equal to 25 with a remainder of 1.

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Answer:

No. A non-uniform probability is where each outcome does not have the same chance of happening; this is not true of a fair 6-sided die, of which each side has an equal 1/6 probability of being rolled.

[tex]\Large\boxed{\sf uniform\ probability}[/tex]

A unique integer value appears on each side. Rolling the die and getting any particular number has a 1/6 chance of happening. There are six outcomes, each uniformly distributed while rolling the dice. Each has an equal probability of occurring.

Answer:

its the thrid one i think i might be wrong srry

Step-by-step explanation:

Answer:

20/53

Answer number 4

Step-by-step explanation:

There are 20 brown, 16 orange, 4 navy, and 13 purple marbles. A marble is drawn at random. What is the probability the marble is brown?

Let's first add the marbles together.

20+16+4+13=53

there are 53 marbles altogether.

20 of the marbles are brown.

So the probability of drawing a brown marble is 20/53

Given:

The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back in 3 hours.

Required:

What is the speed of the boat in still water?

Explanation:

A boat has to travel 8 miles against the current and 8 miles with the current.

Ustream(against the current) the boat's speed is:

speed in still water - current OR x - 2.

Downstream( with the current) the speed is:

speed in still water + current speed OR x + 2.

We know the distance

OR

The total time is 3 hours

The time upstream + The time downstream = 3 hours

a) The original claim expressed in symbolic form is; p > 0.032

b) The hypotheses are defined as;

Null hypothesis; H₀: p ≤ 0.032

Alternative hypothesis; Hₐ: p > 0.032

A hypothesis is defined as an educated guess while using reasonable thinking, about the answer to a scientific question.

a) We are told that the claim is that more than 3.2% (0.032) of homes have only a landline telephone and no wireless phone. Thus, the original claim in symbolic form is; p > 0.032

b) From the sample survey that we see, it is clear that among 15800 homes, 5.81% had landline phones without wireless phones. This would be the sample proportion.

This means that we can define the alternative hypothesis as;

Hₐ: p > 0.032

Null hypothesis is;

H₀: p ≤ 0.032

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Answer:

Slope is 3/8.  m = 4-1 / 3 - (-5) = 3/8

Step-by-step explanation: