Can someone please help me?? Im not quite sure how to get this answer.

What is the area of the shaded region in the figure below? Leave answer in terms of pi and in simplest radical form.

Answer:

[tex]h=\frac{SA-2s^2}{4s}[/tex]

Step-by-step explanation:

we know that'

The formula to calculate the surface area of a square prism is

[tex]SA=2s^2+4sh[/tex]

where

s is the length of the side of the square base

h is the height of the prism

Solve for h

That means ----> Isolate the variable h

so

subtract 2s^2 both sides

[tex]SA-2s^2=4sh[/tex]

Divide by 4s both sides

[tex]\frac{SA-2s^2}{4s}=h[/tex]

Rewrite

[tex]h=\frac{SA-2s^2}{4s}[/tex]

To find the height of a square prism when given the surface area and base side length, use the formula B. H = (SA - 2s^2) / (4s).

The question asks for a formula that can be used to find the height (h) of a square prism given the surface area (SA) and the side length of the base (s). The surface area of a square prism is calculated using the formula SA = 2s2 + 4sh. To solve for h, we need to re-arrange this equation:

Therefore, the correct formula to find h is B. H = (SA – 2s2) / 4s.

Answer:

Dα/dt   = 0.079 degree/sec

Step-by-step explanation:

From problem statement, is easy to see, that if point A is ubicated at the top of the telescope,  the shoreline is directly below the woman ( point B), and the point where the boat is, which is at distance x from shoreline  is point C. These three point  shape a right triangle with angle α (the angle of the telescope).

So we have

tan α  =  x/250    

Differentiating both sides of the equation we get

D (tan α)/dt    =  ( 1/250)* Dx/dt

sec² α Dα/dt  =  ( 1/250)* Dx/dt  

we already know that    Dx/dt   = 20 feet/sec

sec² α Dα/dt  =  20/250   ⇒     sec² α Dα/dt  = 0.08  

Dα/dt   =  0.08 / sec² α

Then

tan α  =  20/250  = 0,08        α   = arctan 0.08      α  ≈ 5⁰

Dα/dt   =  0.08/ sec² α  

From tables we get    cos  5⁰  =  0.9961  then

1/ 0.9961  = 1.003

sec α  = 1.003      and     sec²  α   =   1.0078

Dα/dt   =  0.08/ sec² α    ⇒   Dα/dt   =  0.08/1.0078

Dα/dt   = 0.079 degree/sec

The change of position of the boat results in a change of the angle of the telescope, which can be calculated using related rates. With known factors such as the speed of the boat and its distance from shore, the rate of change of the telescope's angle can be found using the principles of trigonometry and calculus.

This question is about related rates in calculus.  Related rates describe the relationship between different rates of change that are connected to each other. In this case, the changing position of the boat creates a change in the angle of the telescope.

We know the woman is watching a boat that is approaching a shoreline directly below her at 20 feet per second, and we are asked to find the rate that the angle of the telescope is changing when the boat is 250 feet from shore. Here is a way of visualizing it:

Let D be the distance of the boat from the base of the cliff and θ the angle that the telescope makes with the horizontal. We are given that D(t) decreases at 20 feet per second and that when D(t) = 250, we want to know what is dθ/dt.

By using trigonometry, we can find a relationship between D and θ. Specifically, tan(θ) = 250/D, so by implicit differentiation, (sec^2(θ)) * dθ/dt = -250/D^2 * dD/dt. From the given data, dD/dt = -20 and D = 250, so substitute them into the equation and evaluate θ using the tan–1(1) to obtain dθ/dt.

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Answer:

Remainder would be [tex]5x^2+21[/tex]

Step-by-step explanation:

Given,

Dividend = [tex]x^5+x^4+x^3+x^2+x[/tex]

Divisor = [tex]x^3-4x[/tex]

Using long division ( shown below ),

We get,

[tex]\frac{x^5+x^4+x^3+x^2+x}{x^3-4x}=x^2+x+5+\frac{5x^2+21}{x^3-4x}[/tex]

Therefore,

Remainder would be [tex]5x^2+21[/tex]

Answer:

0.2288

Step-by-step explanation:

This is straightforward.

What we need to do is to divide the number of defective semiconductor chips over the total number of semiconductor chips.

Initially, the total number of semi conductor chips is 119 and the total number of defective semiconductor chips is 28.

After the first selections , we can infer that the total number of semiconductor chips is 118 while the number of defective ones is 27.

Hence on the second drawing, the probability that he will

Select a defective one is 27/118

Answer:

(1) Insufficient data

(2) Sufficient data

Step-by-step explanation:

We need to check whether the given data is sufficient or not to prove that a rectangular region has perimeter P inches and area A square inches, is the region square.

Assume that the given conditions are

1. [tex]P=\frac{4}{3}A[/tex]

2. [tex]P=4\sqrt{A}[/tex]

Area of square is

[tex]A=a^2[/tex]

Taking square root on both sides.

[tex]\sqrt{A}=a[/tex]             .... (1)

where a is side length.

Perimeter of square is

[tex]P=4a[/tex]            ... (2)

From (1) and (2) we get

[tex]P=4\sqrt{A}[/tex]

It means second condition is sufficient to prove that the rectangle reason is square, because it is true for all.

For a=3,

A=9 and P=12

[tex]12=\frac{4}{3}(9)[/tex]

[tex]12=12[/tex]

LHS=RHS

For a=6,

A=36 and P=24

[tex]24=48[/tex]   (False statement)

The first condition is insufficient because it may or may not be true.

Answer:

The new crew and the experience crew working together can paint the apartment in 4 hours.

Step-by-step explanation:

Given:

Time taken by new crew of painters to paint an apartment = 12 hours

Time taken by experience crew of painters to paint an apartment = 6 hours

To find the time taken by them to  paint the apartment working together.

Solution:

Using unitary method to determine their 1 hour work.

In 12 hours the new crew can paint = 1 apartment

So,in 1 hours the new crew can paint = [tex]\frac{1}{12}[/tex] of the apartment

In 6 hours the experience crew can paint = 1 apartment

So,in 1 hour the experience crew can paint = [tex]\frac{1}{6}[/tex] of the apartment

Now, the new crew and the experience crew are working together.

So, in 1 hour, they can paint :

⇒ [tex]\frac{1}{12}+\frac{1}{6}[/tex]

Taking LCD = 12, we will add fraction.

⇒ [tex]\frac{1}{12}+\frac{2}{12}[/tex]

⇒ [tex]\frac{3}{12}[/tex]

Simplifying fraction we have:

⇒ [tex]\frac{1}{4}[/tex] of an apartment

Again using unitary method to determine the time taken by them working together to paint the whole apartment.

They can paint  [tex]\frac{1}{4}[/tex] of an apartment in 1 hour.

To paint 1 apartment they will take  = [tex]\frac{1}{\frac{1}{4}}=4[/tex] hours

Thus, the new crew and the experience crew working together can paint the apartment in 4 hours.

Answer:

The answer to your question is letter A

Step-by-step explanation:

Process

1.- Find two points of the line

 A ( -2, 0)

 B ( 0, 3)

2.- Find the slope

     [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

            [tex]m = \frac{3 - 0}{0 + 2}[/tex]

                   [tex]m = \frac{3}{2}[/tex]

3.- Find the equation of the line

            y - y1 = m(x - x1)

            y - 0 = [tex]\frac{3}{2} (x + 2)[/tex]

            y = [tex]\frac{3}{2} (x + 2)[/tex]

Simplify

            y = [tex]\frac{3}{2} x + 3[/tex]

Answer:

The sprinkler must rotate by an angle of 107.48°.

Step-by-step explanation:

Given:

Area of strawberry patch( in shape of sector)  = 1500 square yards

Radius of circle = 40 yards

To find angle through which the sprinkler should rotate.

Solution.

In order to find the angle of rotation of sprinkler, we will apply the area of sector formula.

[tex]Area\ of\ sector\ = \frac{\theta}{360}\times \pi r^2[/tex]

where [tex]\theta[/tex] is the angle of the sector formed and [tex]r[/tex] is radius of the circle.

Thus, we can plugin the given values to find [tex]\theta[/tex] which would be the angle of rotation.

[tex]1500 = \frac{\theta}{360}\times \pi (40)^2[/tex]

Taking [tex]\pi=3.14[/tex]

[tex]1500 = \frac{\theta}{360}\times \ (3.14) (40)^2[/tex]

[tex]1500 = \frac{\theta}{360}\times 5024[/tex]

Dividing both sides by 5024.

[tex]\frac{1500}{5024} = \frac{\theta}{360}\times 5024\div 5024[/tex]

Multiplying both sides by 360.

[tex]\frac{1500\times 360}{5024} =\frac{\theta}{360}\times 360[/tex]

[tex]107.48=\theta[/tex]

∴ [tex]\theta= 107.48\°[/tex]

Angle of rotation of sprinkler = 107.48°

The strawberry farmer needs the sprinkler to rotate approximately 107.46 degrees to cover the 1500 square yard sector of the circle with a 40-yard radius.

To determine the angle through which the sprinkler should rotate, we first need to find the area of the sector of the circle. The formula for the area of a sector is:

A = 0.5 × r² × θ

where A is the area, r is the radius, and θ is the angle in radians. Here, we know the area A is 1500 square yards and the radius r is 40 yards. Rearranging the formula to solve for θ gives:

θ = (2 × A) / r²

Substituting the given values:

θ = (2 × 1500) / 40²

θ = (3000) / 1600

θ = 1.875 radians

To convert this angle in radians to degrees, we use the conversion factor 180/π:

θ = 1.875 × (180 / π) ≈ 107.46 degrees

Therefore, the sprinkler should rotate through an angle of approximately 107.46 degrees.

Answer:

The answer to your question is

a) Poster             width = 3 in

                            lenght = 9 in

b) banner

                           width = 2 in

                           lenght = 10 in

Step-by-step explanation:

a) For the poster

   width = x

   lenght = 3x

Perimeter of a rectangle = 2base + 2 height

                                         = 2(x) + 2(3x) = 24

                                         2x + 6x = 24

                                         8x = 24

                                           x = 24/8

                                           x = 3

    width = 3 in

     lenght = 3(3) = 9 in

b) For the banner

    width = y

    lenght = 5y

Perimeter of a banner = 2 base + 2 height

                                        2 (y) + 2(5y) = 24

                                        2y + 10y = 24

                                        12y = 24

                                           y = 24/12

                                           y = 2

     width = 2 in

     lenght = 5(2) = 10 in

Answer:

11 positive integers can be expressed.

Step-by-step explanation:

Consider the provided information.

The number of possible prime numbers are 5,7,11,and 13.

There are 4 possible prime numbers.

How many positive integers can be expressed as a product of two or more of the prime numbers, that means there can be product of two numbers, three number or four numbers.

The formula to calculate combinations is: [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

The number of ways are:

[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}[/tex]

[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1[/tex]

[tex]^4C_2+^4C_3+^4C_4=6+4+1[/tex]

[tex]^4C_2+^4C_3+^4C_4=11[/tex]

Hence, 11 positive integers can be expressed.

Answer:

(-2,-11)

Step-by-step explanation:

x = -2

y = -11

Answer:

[tex]n=2^4 3^4 5^2 =32400[/tex] and then we have:

[tex]\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432[/tex]

Step-by-step explanation:

From the info given by the problem we need an integer defined as the smallest positive integer that is a multiple of 75 and have 75 positive integral divisors, and we are assuming that 1 is one possible divisor.

Th first step is find the prime factorization for the number 75 and we see that

[tex]75=3 5^2[/tex]

And we know that 3 =2+1 and 5=3+2 and if we replace we got:

[tex] 75 = (2+1)(4+1)^2 = (2+1)(4+1)(4+1)[/tex]

And in order to find 75 integral divisors we need to satisify this condition:

[tex]n= a^{r_1 -1}_1 a^{r_2 -1}_2 *......[/tex] such that [tex]a_1 *a_2*....=75[/tex]

For this case we have two prime factors important 3 and 5. And if we want to minimize n we can use a prime factor like 2. The least common denominator between 2 and 4 is LCM(2,4) =4. So then the need to have the prime factors 2 and 3 elevated at 4 in order to satisfy the condition required, and since 5 is the highest value we need to put the same exponent.

And then the value for n would be given by:

[tex]n=2^4 3^4 5^2 =32400[/tex] and then we have:

[tex]\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432[/tex]

The smallest positive integer that is a multiple of 75 is 32400 and

integral divisors are 432.

Positive integers are the whole number that is greater than zero and do not include decimal or fraction values.

Find the smallest positive integer that is a multiple of 75 that has exactly 75 positive integral divisors.

We know that

[tex]75 = 3*5^{2}[/tex]

So the value of n which has 75 divisors then the multiplication of power of prime factor should be 75. The formula is given by

[tex]n = 2^{x-1} *3^{y-1} *5^{z-1}[/tex]

then the multiplication of x, y, and z must be 75.

x, y, and z are 5, 5, and 3 will be the values.

[tex]n = 2^{4} *3^{4} *5^{2} = 32400[/tex]

And it is divisible by 75 also.

[tex]\dfrac{n}{3*5^{2} } = \dfrac{2^{4} *3^{4} *5^{2}}{3*5^{2} } = 432[/tex]

Thus,  the smallest positive integer that is a multiple of 75 is 32400 and integral divisors are 432.

More about the Integer link is given below.

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The cost of the bike for the given condition will be $230.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose the cost of one bike is x while accessories for one bike is y.

As per the given,

x + y = 276

The cost of bike is 5 times more then accessories,

x = 5y

5y + y = 276

6y = 276

y = 46

Bike cost = 5(46) = $230

Hence "The bike will cost $230 in the specified condition".

For more about the equation,

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Answer:

15 students visited both museums.

Step-by-step explanation:

Operations With Sets

Sets are a collection of elements. Some sets have elements in common with other sets. These elements are said to be in their intersection. If we know the number of elements in the set A and in the set B, and also the total number of elements in both sets, we can say

[tex]N(A\bigcup B)=N(A)+N(B)-N(A\bigcap B)[/tex]

where [tex]N(A\bigcup B)[/tex] is the total number of elements, N(A) and N(B) are the number of elements in A and B respectively, and [tex]N(A\bigcap B)[/tex] is the number of elements in their intersection. If we wanted to know that last number, then we isolate it

[tex]N(A\bigcap B)=N(A)+N(B)-N(A\bigcup B)[/tex]

Let A= Students who visited the museum of natural history

B=Students who visited the natural air and space museum

We know [tex]N(A)=18, N(B)=22, N(A\bigcup B)=25,\ so[/tex]

[tex]N(A\bigcap B)=18+22-25=15[/tex]

Answer: 15 students visited both museums.

Note: We are assuming no students didn't visit at least one museum

The set theory in Mathematics implies that 15 out of the 25 students must have visited both the Museum of Natural History and Natural Air and Space Museum, since these students are counted twice when you add the students who visited each museum separately.

The problem asked is: When 25 students went to Washington DC, 18 of them visited the Museum of Natural History and 22 visited the Natural Air and Space Museum. How many students visited both museums?

To answer this, we need to understand the concept of the set theory in Mathematics. It helps us know the total number of students who visited both museums: we subtract the total number of students from the sum of students who visited each museum separately.

So, if we add those who visited the Museum of Natural History (18 students) and those who went to the Natural Air and Space Museum (22 students), we get 40. But we know there were only 25 students in total, implying that 15 students must have visited both museums since these students are counted twice in our sum. Therefore, 15 students visited both museums.

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Answer:

Step-by-step explanation:

Annual interest rate is 2.75%. Hence, the monthly interest rate is [tex]\frac{2.75}{12}[/tex]

The amount will be compounded [tex](20\times12) = 240[/tex] times.

Every month they deposits $500.

In the first month that deposited $500 will be compounded 240 times.

It will be [tex]500\times [1 + \frac{2.75}{1200} ]^{240}[/tex]

In the second month $500 will be deposited again, this time it will be compounded 239 times.

It will give [tex]500\times [1 + \frac{2.75}{1200} ]^{239}[/tex]

Hence, the total after 20 years will be [tex]500\times [1 + \frac{2.75}{1200} ]^{240} + 500\times [1 + \frac{2.75}{1200} ]^{239} + ........+ 500\times [1 + \frac{2.75}{1200} ]^{1} = 160110.6741[/tex]

The account will have approximately $159,744.59 after 20 years.

To calculate the future value of the savings account after 20 years with a 2.75% annual interest rate compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

Plugging in the values, we can calculate:

A = 500(1 + 0.0275/12)^(12*20)

A = 500(1.00229167)^(240)

A ≈ $159,744.59

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Answer:

[tex]P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}[/tex]

Step-by-step explanation:

In a coin toss the  probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

[tex]R=\frac{2n!}{m!*(2n-m)!}[/tex]

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of [tex]P_{case}=0.5^{2n}[/tex] so:

[tex]P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}[/tex]

For example, to toss 4 heads in 5 rounds:

[tex]P=\frac{10!}{4!*(10-4)!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7*6!}{4!*6!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7}{4!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7}{4!}*0.5^{10}=0.205[/tex]

Answer:

  E.  1/2

Step-by-step explanation:

Divide by 2, then make use of the Pythagorean identity for sine and cosine.

  sin(x)^2 +cos(x)^2 = 2a

  1 = 2a . . . . . . . sin²+cos²=1

  1/2 = a

Answer:

Option E) is correct.

[tex]a=\frac{1}{2}[/tex]

Step-by-step explanation:

Given trignometric equation is [tex]2sin^{2}x + 2cos^{2}x = 4a[/tex]

To find the value of "a" from the given equation:

[tex]2sin^{2}x + 2cos^{2}x = 4a[/tex]

Taking common number "2" outside the equation of left hand side

[tex]2(sin^{2}x +cos^{2}x) = 4a[/tex]

[tex]sin^{2}x +cos^{2}x =\frac{4a}{2}[/tex]

[tex]sin^{2}x+cos^{2}x =2a[/tex]

( We know the trignometric formula  [tex]sin^{2}\theta +cos^{2}\theta=1[/tex] here

[tex]\theta=x[/tex]  )

Therefore  [tex](1) =2a[/tex]

[tex]\frac{1}{2} =a[/tex]

It can be written as

[tex]a=\frac{1}{2}[/tex]

Therefore  [tex]a=\frac{1}{2}[/tex]

Option E) is correct.

the answer of this question is 603.2yd2

Answer:Area of the shaded region is 603.2 yards^2

Step-by-step explanation:

The diagram contains two circles. The smaller circle has a radius of 8 yards.

The bigger circle has a radius of 16 yards.

The area of a circle is expressed as

Area of circle = πr^2

Where

r = radius of circle

π is a constant whose value is 3.142

The area of the smaller circle would be

3.142 × 8^2 = 201.088 yards^2

The area of the bigger circle would be

3.14 × 16^2 = 804.352 yards^2

Area of the shaded region would be area of the bigger circle - area of the smaller circle. It becomes

804.352 - 201.088 = 603.2 yards^2

Answer:

[tex]P(X\geq 5)=1-P(X< 5)=1-[0.000649+0.00703+0.0343+0.0991+0.1878]=0.6712[/tex]

Step-by-step explanation:

1) Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

2) Solution to the problem  

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=10, p=0.52)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

What is the probability that at least 5 of the students in your study group of 10 have studied in the last week?

[tex]P(X\geq 5)=1-P(X< 5)=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)][/tex]

[tex]P(X=0)=(10C0)(0.52)^0 (1-0.52)^{10-0}=0.000649[/tex]  

[tex]P(X=1)=(10C1)(0.52)^1 (1-0.52)^{10-1}=0.00703[/tex]  

[tex]P(X=2)=(10C2)(0.52)^2 (1-0.52)^{10-2}=0.0343[/tex]  

[tex]P(X=3)=(10C3)(0.52)^3 (1-0.52)^{10-3}=0.0991[/tex]  

[tex]P(X=4)=(10C4)(0.52)^4 (1-0.52)^{10-4}=0.1878[/tex]  

[tex]P(X\geq 5)=1-P(X< 5)=1-[0.000649+0.00703+0.0343+0.0991+0.1878]=0.6712[/tex]

To find the probability that at least 5 of the students in a study group of 10 have studied in the last week, use the binomial probability formula and calculate the respective probabilities for each case. Add these probabilities together to get the final probability.

To calculate the probability that at least 5 of the students in your study group of 10 have studied in the last week, we can use the binomial probability formula. Let's denote the probability that a randomly selected teenager studied at least once during the week as p = 0.52. We want to find P(X >= 5) where X represents the number of teenagers in the study group who studied.

Using the binomial probability formula, P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10). We can calculate each of these individual probabilities using the formula: [tex]P(X = k) = C(n, k) * p^k * (1-p)^(^n^-^k^),[/tex] where C(n, k) is the combination of n items taken k at a time.

Once we have calculated each of these probabilities, we can add them together to find the final probability.

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Answer:

D

Step-by-step explanation:

Finding y int by substituting the points given (say y int is x)

(-9) = 4(-4) + x

(-9) = -16 + x

x = 7

With the y int, you can now write the equation

y = -4x + 7

The equation of the line will be y = –4x + 7 having a slope of –4 that passes through the point (4, –9). Option D is correct.

To find the equation of a line that has a slope of –4, and includes the point (4, –9), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plugging in our values, we get y - (-9) = -4(x - 4). Simplifying this, we have:

Subtract 9 from both sides to solve for y:

Thus, the correct equation is y = –4x + 7.

Hence, D. is the correct option.

Answer: the number of new light bulbs that they put in is 36

Step-by-step explanation:

The Marino's put new light bulbs in all the fixtures the new house.

Each fixture used 2 light bulbs and each room had 3 fixtures. This means that the number of bulbs in each room would be 3×2 = 6 bulbs.

The new house had 6 rooms. This means that the total number of bulbs in 6 rooms would be

6 × 6 = 36 bulbs

Answer:

[tex]p_v =2*P(Z>4.21) =2.55x10^{-5}[/tex]

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example[tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

D) Are statistically different.

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]  

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]  

Or equivalently:  

Null hypothesis: [tex]\mu_1 - \mu_2 = 0[/tex]  

Alternative hypothesis: [tex]\mu_1 -\mu_2\neq 0[/tex]  

Where [tex]\mu_1[/tex] and [tex]\mu_2[/tex] represent the percentages that we want to test on this case.

The statistic calculated is on this case was Z=4.21. Since we are conducting a two tailed test the p value can be founded on this way.

[tex]p_v =2*P(Z>4.21) =2.55x10^{-5}[/tex]

And we can use the following excel code to find it:"=2*(1-NORM.DIST(4.21,0,1,TRUE)) "

With the p value obtained and using the significance level assumed for example[tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the percentage 1 is significantly different from the percentage 2.

And the best option on this case would be:

 D) Are statistically different.

Answer:

C. $144,200

Step-by-step explanation:

We have been given that a borrower's monthly interest payment on an interest-only loan at an annual interest rate of 7.3% is $877.

To find the loan amount, we will use simple interest formula.

[tex]I=Prt[/tex], where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

One month will be equal to 1/12 year.

[tex]7.3\%=\frac{7.3}{100}=0.073[/tex]

Upon substituting our given values in simple interest formula, we will get:

[tex]877=P*0.073*\frac{1}{12}[/tex]

[tex]877*12=P*0.073*\frac{1}{12}*12[/tex]

[tex]10524=P*0.073[/tex]

[tex]P*0.073=10524[/tex]

[tex]\frac{P*0.073}{0.073}=\frac{10524}{0.073}[/tex]

[tex]P=144164.3835616438356[/tex]

Upon rounding to nearest hundred, we will get:

[tex]P\approx 144,200[/tex]

Therefore, the loan amount was $144,200 and option C is the correct choice.

Final answer:

To calculate the loan amount based on a monthly interest payment and an annual interest rate, convert the rate to monthly and divide the payment by this rate. For a monthly payment of $877 at 7.3% annual interest, the loan amount is approximately $144,200.

Explanation:

To determine the loan amount of an interest-only loan given a monthly interest payment and an annual interest rate, follow these steps:

In this case, the annual interest rate is 7.3%, so the monthly interest rate is 7.3% / 12 = 0.6083%. The monthly interest payment is $877. Therefore, the loan amount can be calculated as follows:

$877 / 0.6083% = $877 / 0.006083 = $144,200.46

When rounded to the nearest hundred, the loan amount is $144,200.

The correct answer is C. $144,200.

Answer:

Step-by-step explanation:

Mrs Cain coleslaw recipe calls for 1/3 cup of oil, 1/2 cup of vinegar, 1/4 cup of sugar. This means that the ratio of the number of cups of oil to vinegar to sugar is 1/3 : 1/2: 1/4

If she has 1 cup of vinegar, the ratio that would correspond to the given ratio would be determined by multiplying the given ratio by 2. It becomes, 2/3 : 2/2 : 2/4 = 2/3 : 1 : 1/2

Therefore, she would require 2/3 cups if oil and 1/2 cups of sugar to make 1 batch.

Answer:

[tex]a_{n+1}=0.2a_n[/tex] for all n>0, [tex]a_1=16[/tex]

Step-by-step explanation:

Let [tex]\{a_n\}=\{16,3.2,0.64,0.128,\cdots \}[/tex] be the sequence described.

A geometric sequence has the following property: there exists some r (the ratio of the sequence) such that [tex]\frac{a_{n+1}}{a_n}=r[/tex] forr all n>0.

To find r, note that

[tex]\frac{3.2}{16}=\frac{32}{10(16)}=\frac{2}{10}=\frac{1}{5}=0.2[/tex]

Similarly

[tex]\frac{0.64}{3.2}=\frac{64}{10(32)}=\frac{1}{5}=0.2[/tex]

[tex]\frac{0.128}{0.64}=\frac{1}{5}=0.2[/tex]

Thus [tex]a_{n+1}=r a_n=\frac{a_n}{5}=0.2a_n[/tex] for all n>0, and [tex]a_1=16[/tex]

first term = 16

average ratio = 0.2

Answer:

Step-by-step explanation:

Total number of Pokemon cards that Tim has in his collection is 480

He arranges the cards in his album and each page of his album holds 12 cards.

The total number of pages in the album is 35. After he has filled his album completely, the total number of cards that the album would contain would be 35 × 12 = 420

Let x represent the number of Pokemon cards he has left. Therefore, the expression becomes

x + 420 = 480

x = 480 - 420 = 60

The store received 1725 pencils and 1350 pens as of the given conditions.

Given that,
A store receives a shipment of pens and pencils. Each box contains 75 items There are 23 boxes of pencils and 18 boxes of pens. How many pens and pencils the store receive is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Each box contains 75 items,
The number of item in 23 pencil boxes = 75 × 23 = 1725 items,
The number of items in 18 pencil boxes = 18 × 75 = 1350 items.

Thus, the store received 1725 pencils and 1350 pens as of the given conditions.

Learn more about arithmetic here:

https://brainly.com/question/11424589

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Answer: confidence interval = 27.5 +/- 1.68

= ( 25.82, 29.18)

Step-by-step explanation:

Given;

Number of samples n = 64

Standard deviation r = 6mi/gallon

Mean x = 27.5mi/gallon

Confidence interval of 97.5%

Z' = t(0.0125) = 2.24

Confidence interval = x +/- Z'(r/√n)

= 27.5 +/- 2.24(6/√64)

= 27.5 +/- 1.68

= ( 25.82, 29.18)

Answer:

P(X1=1, X2=1) = 1/15

P(X1=1, X2=0) = 7/30

P(X1=0, X2=1) = 7/30

P(X1=0, X2=0) = 7/15

Step-by-step explanation:

Let Xi = 1 if the i-th white ball is selected. In this question the 3 white balls are marked 1,2 and 3.

We need to know the possible combination between X1 and X2 i.e. for the white ball 1 and 2 being chosen in the event.

We also need to note that the event is dependent which that after a ball is being chosen, it will not be put back hence affecting the probability of picking the next ball.

Consider all the possible combination between X1 and X2

a) both being chosen P(X1=1, X2=1)

= (3/10) x (2/9) = 1/15

Note that the first probability is the probability before any ball is being picked. The chances for ball white to be pick is 3/10 (3 white ball from the total 10 balls).

After 1 white ball being selected, that ball is not again out back into the urn making white ball 2 and total ball 9. Hence probability of picking another white ball is 2/9

b) only X1 chosen P(X1=1, X2=0)

= (3/10) x (7/9) = 7/30

After the white ball was picked, the probability of white not being pick again is the same as red being picked. Since there is still 7red balls and a total of 9 balls, the probability is 7/9

c) only X2 chosen P(X1=0, X2=1)

= (7/10) x (3/9) = 7/30

The white is not being picked first, making the probability of picking red is 7/10. Then the probability of white being picked is 3/9

d) both not chosen

P(X1=0, X2=0)

= (7/10) x (6/9) = 7/15

In other word only red being chosen. So the first probability is 7 red out of 10 balls (7/10), and the next red ball being picked next is 6/9

Good evening ,

Answer:

2x² - 18x + 36

Step-by-step explanation:

2(x-3)(x-6) = 2x²-18x+36.

:)