A genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 153 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{\frac{7}{2}})\qquad (\stackrel{x_2}{\frac{5}{3}}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(\frac{5}{3}-2)^2 + (1-\frac{7}{2})^2}\implies d=\sqrt{(\frac{-1}{3})^2 + (-\frac{5}{2})^2} \\\\\\ d=\sqrt{\cfrac{1}{9}~~ + ~~\cfrac{25}{4}}\implies d=\sqrt{\cfrac{229}{36}}\implies d=\cfrac{\sqrt{229}}{\sqrt{36}}\implies d=\cfrac{\sqrt{229}}{6}[/tex]

The formula for the area(A) of the sector is,

Given:

Therefore,

Simplify

Hence,

The Simple interest after three month $423.70

What is Simple Interest ?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

If she deposits $366 in the account and you receive interest, you must first calculate the interest for the current year before adding the sum to calculate the interest for the following month.

for instance, deposit plus interest equals the new amount for month one, month one amount plus interest equals amount for month two, and month two amount plus interest equals amount for month three.

The total would thus be $423.70 for the following month:

month 1

366+ (366*.05)=x

366+18.3=x

month 2

384.30+(384.30*.05)=x

384.30+19.22=x

month 3

403.52+(403.52*.05)=x

403.52+20.18=x

423.7 = x

Thus, total amount then would be $423.70

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EXPLANATION

To solve the given equation:

Step 1:

Multiply both-side of the equation by 2 in other to eliminate the denominator.

At the right-hand side of the equation, 2 add the numerator will cancel-out 2 at the denominator.

- 8 = v+ 6

step 2:

Subtract 6 from both-side of the equation.

That is;

-8 - 6 = v + 6 - 6

-14 = v

Hence, the value of v = -14

iven:

he fucnction is,

xplanation:

he graph fo the function cnan be obtained by graph of cube root of x.

If we shift the graph of cube root by x by one unit left then then function changed to,

If the obtained graph shrink vertically by a factor of 3/4 then graph changed to function,

This is the requied function for which we need the graph.

So graph can be obtained by horizontal shift of 1 unit to left, shrink by a factor of 3/4 and there is no vertical shift and graph will not flip over any axis.

Thus answer is, All statements are true.

The amount earned by $3000 deposited in the account after 6 months is $60.30

What does quarterly compounding mean?

Quarterly compounding means that the interest is computed and credited to the account every quarter, that is every 3 months, in other words, our future value formula would indicate quarterly interest rate rather than an annual interest rate

FV=PV*(1+r)^N

FV=the amount in the account after 6 months=unknown\

PV=initial amount deposited in the account=$3,000

r=quarterly interest rate=4%/4=0.01

N=number of quarters in 6 months=2

FV=$3000*(1+0.01)^2

FV=$3000*(1.01)^2

FV=$3000*1.0201

FV=$ 3,060.30

amount earned=FV-PV

amount earned=$3060.30-$3000

amount earned=$60.30

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Step-by-step explanation:

9x + 4y is where (9,4) is the coordinates

Answer:

2.5×10^-11

Step-by-step explanation:

Put the point in the middle of 2 and 5 and count how many times you need to get there ...

like 0.05 to put point after 5 you have to jump 2 steps so it is 5×10^-2.

The length of the rectangle is 3 times it width. The width size is given as 2 inches.

Therefore,

width = 2 inches

length = 3(2) = 6 inches

The area of the rectangle can be calculated below

The answer is B.

Let x represent the number of math problems that you completed.

Let y represent the number of biology problems that you completed

From the information given,

You completed a total of 15 problems. This means that

x + y = 15

If each math problem takes 5 minutes to complete, it means that the time to complete x math problems is 5 * x = 5x

If each biology problem takes 3 minutes to complete, it means that the time to complete y biology problems is 3 * y = 3y

If you spent 51 minutes working on your homework problems for math and

biology, it means that

5x + 3y = 51

Thus, the system of equations is

x + y = 15

5x + 3y = 51

Step-by-step explanation:

Let use the following rules to construct a polynomial,

Rule 1:

If r is a zero of some polynomial, f(x), then

[tex](x - r)[/tex]

is a factor of the polynomial

We first know that one of our zeroes are real, which is 0.

So since r=0

[tex](x - 0) = x[/tex]

is a factor

However, since the root ,0, has a multiplicty of 4, that basically means we have 0 as a root 4 times or basically we multiply the factor 4 times.

[tex]x \times x \times x \times x = x {}^{4} [/tex]

This leads to an another rule:

If a polynomial has a zero, r that has a multiplicty of k,

we represent the factor as

[tex](x - r) {}^{k} [/tex]

where k is all integers greater than 0.

So to reinforce myself, since 0 has a multiplicty of 4, we have

[tex](x - 0) {}^{4} = {x}^{4} [/tex]

So our first factor is

[tex] {x}^{4} [/tex]

Part 2: Complex Zeroes.

When dealing with complex zeroes, we must note this rule.

if (a+bi) is a zero of some polynomial, p then its conjugate (a-bi) is a factor as well.

So if 3-2i is a factor, then

3+2i is a factor as well.

Using Rule 1, our factors now become

[tex](x - (3 + 2i))[/tex]

and

[tex](x - (3 - 2i))[/tex]

So our factors are

[tex] {x}^{4} (x - (3 - 2i)(x - (3 + 2i))[/tex]

To simplify use FOIL Method,

[tex] {x}^{4} ( {x}^{2} - x(3 + 2i) - x(3 - 2i) + 9 - 4 {i}^{2} )[/tex]

[tex] {x}^{4} ( {x}^{2} - 6x + 13)[/tex]

[tex] {x}^{6} - 6 {x}^{5} + 13 {x}^{4} [/tex]

So our polynomial is

[tex] {x}^{6} - 6 {x}^{5} + 13 {x}^{4} [/tex]

There are two possibilities for answers none of which require subtraction based on the expression given:

With the question none of which involves subtraction. First is that this is a simple multiplication in which case the answer is 1,400;

Second that the above expression actually means 14x * 25x * 4 in which case the answer is 1400x²

Explanation 1

14 x 25 x 4

= 350 x 4

= 1,400

Explanation 2

14x * 25x * 4
= 1400 * x * x

= 1400x²

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Surface area of a sphere: 4 π r^2

Where:

r = radius = d/2 = 14/2 = 7

Replacing

SA = 4 π 7^2 = 4 π 49 = 196π cm2

Answer:

260+325 = 585

260 where instructors that were full time and 325 were already full time. this is correct if I am reading your question correctly if not the answer is likely 260

An expression exists as a number, a variable, or a combination of numbers and variables, and function symbols. The speed in still water exists 4 mph.

The acronym BODMAS, which stands for brackets of, division, multiplication, addition, and subtraction, might be used to simplify the expression. It specifies how to answer a mathematical expression in a particular order.

Let x be the speed in still water

[tex]$&\frac{5}{x+1}+\frac{6}{x-1}=3[/tex]

LCD = (x + 1)(x - 1)

[tex]$&(x+1)(x-1) \cdot \frac{5}{x+1}+(x+1)(x-1) \cdot \frac{6}{x-1}=(x+1)(x-1) \cdot 3 \\[/tex]

simplifying the above equation, we get

5(x - 1) + 6(x + 1) = 3(x + 1)(x - 1)

5x - 5 + 6x + 6 = 3 x² - 3

3x² - 11x - 4 = 0

(3x + 1)(x - 4) = 0

x = -1/3 (speed is not negative);

then we get x = 4 mph

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The linear function that gives the full-time year-round median salary for U.S. workers in t years after 2000 is given by:

S(t) = 30846 + 1097.7.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

Linear functions are used in situations when the rate of change is constant, or can be interpreted as a constant, and this rate is called the slope, as we stated above.

In this problem, we have that:

Hence the linear function that models the situation is given as follows:

S(t) = 30846 + 1097.7.

The complete problem could not be found on any search engine, hence we are going to suppose that it asks for a linear function for the median salary in t years after 2000.

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Answer:

C' = (13, 4)

Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units right.

Step-by-step explanation:

Given vertices of triangle ABC:

If two triangles are said to be similar:

To keep the corresponding angles of both triangles the same and maintain similarity, dilate triangle ABC.

If we compare the coordinates of B (1, 4) and B' (5, 8), the y-value has been multiplied by 2.

Therefore, the first step of the transformation is a dilation by a scale factor 2 with the origin (0, 0) as the center of dilation.

⇒ (1 × 2, 4 × 2) = (2, 8)

After multiplying the coordinates of B by two, the difference between the x-values of the dilated point and B' is 3, so the second step of the transformation is a translation of 3 units right.

Therefore, the series of transformations is:

Mapping Rule:  (x, y) → (2x+3, 2y)

Therefore, the coordinates of point C' are:

⇒ C' = (2(5) + 3, 2(2)) = (13, 4)

Answer:   (13, 4)

Infinitely many answers are possible.

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

Explanation:

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because I'll be using the same steps and ideas. There are also diagrams that might help visualize what's going on.

---------

The translation vector from B(1,4) to C(5,2) is <4,-2> since we move to the right 4 units, and down 2 units. It's the shorthand way of writing [tex](x,y) \to (x+4,y-2)[/tex]

Double the coordinates of the translation vector <4,-2> to get <8,-4>

If we started at point B'(5,8) and followed the pathway "right 8, down 4" then we arrive at C'(13,4) as one possible answer.

We could express the steps like this

[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}-4)\\\\(5,8)\to(5+8,8-4)\\\\(5,8)\to(13,4)\\\\[/tex]

As I mentioned in the link above, there are infinitely many answers because we can change the scale factor to any nonnegative real number. For instance we could triple the coordinates of <4,-2> to get <12,-6> and follow the same outline of steps to get C'(17,2) as another possible answer.

First, find the actual number of miles per round trip in each case.

-Hyperloop

-Airplane

Then, the cost (round trip) would be related to the constant b in both cases since it is a fixed rate. Multiply it by the maximum number of passengers,

Then, multiply the rate of consumption by the fuel costs for each mean of transportation,

Notice that it is multiplied by 2 since the rate of consumption row is given in one-way unitsThus,

The probability she will need to attend more than 3 try-outs is 0.7049.

The probability of an actress getting a job after a tryout is 0.11.

The actress wants to keep trying out for new jobs until she gets offered one.

The number of trials necessary for success in a series of independent trials follows a geometric distribution with parameter p, where p is the probability of success in a single trial.

The probability mass function is given as:

[tex]P(X=k)=q^{k-1}p[/tex] where k = 1, 2, 3

We have p = 0.11

q = 1 - 0.11 = 0.89

If X is the number of tryouts,

[tex]P(X=k)=q^{k-1}p\\P(X=k)=(0.89)^{k-1}(0.11)[/tex]

[tex]P(X\leq r)=1-q^r\\P(X\leq r)=1-(0.89)^r[/tex]

Therefore, the probability that she will need to attend more than 3 try outs will be:

P = P( X > 3 )

P = 1 - P( X ≤ 3 )

P = 1 - [ 1 - 0.89³ ]

P = 1 - 1 + 0.89³

P = 0.704969

P = 0.7049

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Step-by-step explanation:

you would take half of 15 and then square it to get to number, which is 56.25

Answer:

[tex](\frac{15}{2} )^2=\frac{225}{4}[/tex]

Step-by-step explanation:

[tex]x^2+15x-23=0\\x^2+15x+(\frac{15}{2} )^2-(\frac{15}{2})^2-23=0\\(x^2+15x+(\frac{15}{2})^2)=23+(\frac{15}{2})^2\\(x+\frac{15}{2})^2=(23*4+15^2)/4=317/4\\x+\frac{15}{2}=+\frac{\sqrt{317}}{4}\\, -\frac{\sqrt{317}}{4}\\\\x=-\frac{15}{2}-\frac{\sqrt{317}}{4}\\\\, -\frac{15}{2}+\frac{\sqrt{317}}{4}\\\\[/tex]

The most appropriate choice for linear equation will be given by -

Kevin is not correct

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here,

Let Kevin has x times as many stamps as stamp

Jackie has 9 stamps

Number of stamps Kevin has = 9x stamps

By the problem,

                          9x = 36

                            [tex]x = \frac{36}{9}[/tex]

                            x = 4

So Kevin has 4 times as many stamps as Jackie

But Kevin says  he has 5 times as many stamps as Jackie.

So Kevin is not correct.

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The game's expected value is -$0.83.

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Domain = the set of possible values along the x axis.

Domain = (-5 , 3 ]

Range = the set of possible values along the y axis.

Range = (-3 , 5 ]

Answer:

Slope: 2

Y-intercept: -3

Step-by-step explanation:

y=2x-3

The slope is always the number(s) before the x and the y-intercept is what is added or subtracted

20 miles per hour converted to feet per second is 88/3 feet per second.

It is given in the question that there are 60 minutes in one hour and 60 seconds in one minute.

We have to convert 20 miles per hour in feet per second.

We know that,

1 mile = 5280 feet

1 hour = 60 minutes

1 minute = 60 seconds

Hence, we can write,

1 hour = 60*60 = 3600 seconds

1 mile per hour = 5280/3600 feet per second = 22/15 feet per second

Using unitary method, we can write,

20 miles per hour = 20*(22/15) = 88/3 feet per second or 29.3334 feet per second.

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If Scampini has no debt or preferred stock, and its WACC is 12%, and it has zero nonoperating assets in which Scampini has 40 million shares of stock outstanding, the stock's value per share is $37.50.

Next year CF = $75 millions

Growth rate of CF = 7%

WACC = 12%

Number of shares outstanding = 40 million shares

Estimated business valuation:

Valuation = Next year CF/ (WACC -growth rate)

Valuation = $75 million / (12% - 7%)

Valuation = $75 million /5%

Valuation =$1500 million

Estimated stock price:

Stock price = Valuation /Shares outstanding

Stock price = $1500 million / 40 million shares

Stock price = $37.50

Therefore the stock price is $37.50.

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Answer:

Write down one equation or inequality that has more than two solutions, but not infinitely many solutions

Step-by-step explanation:

Answer:

AAAAAAAAAA

Step-by-step explanation: AAAAAAAAAAAAAAAA

answer: 4) -10