can someone help me with these questions??? ill give 45 points

1. 5 miles in 1 1/2

2. 2/3 pound for every 1/4 tablespoon

3. 6 pages every 1/5 hour


Marcus can type 40 words in half a minute. Rhys can type 100 words in one and a half minutes. Which student can type at a greater rate of words per minute?

The relation for x and y is given as y = 26/x. The correct answer is option (B).

When two quantities have some dependence in their values they can be said proportional to each other.

It can be of two types such as direct and indirect.

The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.

Given that,

The proportionality relation between x and y as

y ∝ 1/x

And, y = 2 at x = 13.

Suppose k is the constant of proportionality.

Then, y = k/x

Substitute y = 2 and x = 13 in the above equation to obtain,

2 = k/13

=> k = 26

Thus, by substituting the value of k the equation can be written as y = 26/x.

Hence, the equation that relates x and y is y = 26/x.

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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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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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The value of p is 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

Given that

Point A(p8,4p+5) is located on a line that connects M(-2,-5) and N(1,-10).

The equation of line that passing through points  M and N,

Use the formula of equation of line,

y-y₁ = (y₂-y₁/x₂-x₁)(x-x₁)

y-(-5) = (-10+5/1+2)(x-(-2))

⇒ y+5 = -5/3(x+2)

⇒5x+3y +25 = 0    (1)

Since, line passes through point  A(p−8,4p+5), so this point A will satisfy the equation (1)

5(p-8)+3(4p+5)+25 = 0

⇒ 17p = 0

⇒ p = 0

The value of p is 0.

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Draw the picture.

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

-----

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

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

The scientific notation of 69200000 is  6.92 × 10⁷

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number.

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Answer:

10 cm

Step-by-step explanation:

since DE is probably equal to AD which is 17 we subtract the length of the side of CD to find CE

Length CD can be found because it is equal to AB which is 7 cm so we subtract

17-7=10

Hopes this helps please mark brainliest

Answer:

CE = 10

Step-by-step explanation:

Because they are congruent:

AD = 17, that means DE = 17

AB = 7, that means CD = 7

To find what CE is, we start with the full length:

DE

and by subtracting CD (that's part of the length), we can get CE.

DE - CD = CE

Just substitute the values in:

17 - 7 = 10

CE = 10

So there's the answer, but check this out:

CE + CD = DE

10 + 7 = 17

The percentage of confidence intervals that would capture the true population means is approximately 95% of them. which is the correct answer would be option (C).

There were 100 random samples of the same size drawn from a population known to have a normal distribution with a mean and a standard deviation.

For each of the 100 random samples, a 95% confidence interval for the population mean was created.

Since all the conditions are satisfied,

Therefore, the percentage of confidence intervals that would capture the true population means is approximately 95% of them.

Hence, the correct answer would be an option (C).

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Answer:

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

Step-by-step explanation:

Answer:

[tex]2(w-6^2)[/tex]

Step-by-step explanation:

We are doubling the difference, so we first need to find the difference. Our two numbers are [tex]w[/tex] and [tex]6^2[/tex] (you can also write 36 but that is how the problem states it). Therefore, the equation for that is [tex]w-6^2[/tex]. Then, if we double it, we get [tex]2(w-6^2)[/tex].

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:

383.7

Step-by-step explanation:

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

Hopes this helps please mark brainliest

If we use more than 133 minutes then the 2nd plan will be preferable.

Given:

The first plan charges a rate of 26 cents per minute. The second plan charges charges a monthly fee of $19.95 plus 11 cents per minute.

26 cents = $0.26

Let m be the minutes

19.95 + .17m < .32m

Subtract .17m from both sides

19.95 < .32m - .17m

19.95 < .15m

Divide both sides by .15

19.95/.15 < m

133 < m

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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 smallest number is 5, middle number is 8 and largest number is 11.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let x be the smallest number.

let x + 3 be the middle number.

let x + 6 be the largest number.

Then, the equation is

5 (x + 6) = 3 x + 5 (x + 3)

5x+ 30 = 3x+ 5x + 15

3x = 30- 15

3x= 15

x= 5

So, the numbers are x = 5, x + 3 = 8, and x + 6 = 11.

Now, the difference between each succeeding number is 3.

5 x 11 = 55

3 x5 + 5 x 8 = 15 + 40 = 55

Hence, the smallest number is 5, middle number is 8 and largest number is 11.

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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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If all the television at the stores are 3/4 of the original price and has a $40 discount coupon, then the equation which she used to find the price of the television is f = (3/4)p - 40

The original price of the television = p

The 3/4 of the original price = (3/4)p

The worth of the discount coupon = $40

So the discount price will be subtracted

Then, the final price of the television = (3/4) × The original price of the television - The worth of the discount coupon

Substitute the values in the equation

The final price of the television f = (3/4)p - 40

Hence, If all the television at the stores are 3/4 of the original price and has a $40 discount coupon, then the equation which she used to find the price of the television is f= (3/4)p - 40

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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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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 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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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.

The nth term of the sequence is aₙ = 48 + 2n

The definition of the function is given as

a₁= 50

aₙ = aₙ₋₁ + 2

The above definitions imply that we simply add 2 to the previous term to get the current term

Using the above as a guide, we have:

The common difference, d = 2

First term, a = 50

The nth term of the sequence is calculated as

aₙ = a₁ + (n - 1)* d

Substitute the known values in the above equation

So, we have the following representation

aₙ = 50 + (n - 1)* 2

So, we have

aₙ = 50 + 2n - 2

Evaluate the like terms

aₙ = 48 + 2n

Hence, the nth term is aₙ = 48 + 2n

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As per the given matrix A and B, the value of -7A - 6B is [tex]-7A - 6B = \begin{bmatrix} 40 & -106 &-32 \\ -46& 43 &25 \\82 & -62& -22 \end{bmatrix}[/tex]

Matrix:

Basically, a set of numbers arranged in rows and columns so as to form a rectangular array is known as matrix.

Given,

Here we have the matrix A and B.

Now we have to find the -7A - 6B.

In order to solve this matrix, first we have to find the value of -7A,

To find that one, we have to multiply -7 with A,

Then we get,

[tex]-7 \times\begin{bmatrix}-10 &10 &8 \\ -2& -1 &5 \\ -4& 8& -6\end{bmatrix} = \begin{bmatrix}70 &-70 &-56 \\ 14& 7 &-35 \\ 28& -56& 42\end{bmatrix}[/tex]

Similarly, we have to find the value of 6b,

In order to find that, we have to multiply 6 with the matrix B,

Then we get,

[tex]6 \times\begin{bmatrix}5 &6 &-4 \\ 10& -6 &-10 \\ -9& 1& 10\end{bmatrix} = \begin{bmatrix}30 & 36 &-24 \\ 60& -36 &-60 \\ -54& 6& 60\end{bmatrix}[/tex]

Now, we have to subtract the resulting matrix,

[tex]-7A - 6B = \begin{bmatrix}70 &-70 &-56 \\ 14& 7 &-35 \\ 28& -56& 42\end{bmatrix} - \begin{bmatrix} 30 & 36 &-24 \\ 60& -36 &-60 \\ -54& 6& 60 \end{bmatrix}[/tex]

Therefore, the resulting matrix is

[tex]-7A - 6B = \begin{bmatrix} 40 & -106 &-32 \\ -46& 43 &25 \\82 & -62& -22 \end{bmatrix}[/tex]

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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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The monthly payment on the amortized loan is $206.74. The car cost in total is $14, 885. 52. The money paid in interest is $1, 861.52.

The monthly payment is called an annuity because it is constant and remains the same.

Use the present value of an annuity to find the monthly payment to be:

Loan amount = Monthly payment x Present value interest factor of annuity, period, rate

The period is:
= 6 years x 12

= 72 months

The rate is:

= 4.5% / 12 months a year

= 0.375%

The loan amount is:

= 14, 800 x ( 1 - downpayment)

= 14, 800 x ( 1 - 12%)

= $13, 024

The monthly payment is:

13, 024 = Monthly payment x Present value interest factor of annuity, 72 periods , 0.375%

Monthly payment = 13, 024 / 62.995976235992

= $206.74

The car cost in total is:

= Monthly payment x Number of months

= 206. 74 x 72

= $14, 885. 52

The money paid in interest is:

= Loan amount - Car cost

= 14, 885.52 - 13, 024

= $1, 861.52

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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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