The weight of the eggs produced by a certain breed of hen are normally distributed with a mean of 65 grams and standard deviation of 5 grams. What is the probability that a sample of 12 eggs will have a mean weight of more than 68 grams?

A. [tex]\mu[/tex] ≤ 503

B. [tex]\mu[/tex] > 503

C. t = (505 - 503) / (41 / [tex]\sqrt{70}[/tex]) = 1.38

D. The P-value (0.086) is greater than the level of significance (0.05).

A. Null Hypothesis: The mean SAT score of the students who completed the preparation course is not significantly higher than the mean score of 503.

[tex]\mu[/tex] ≤ 503

B. Alternative Hypothesis: The mean SAT score of the students who completed the preparation course is significantly higher than the mean score of 503.

[tex]\mu[/tex] > 503

C. The Value of the test statistic:

We apply the algorithm below to determine the test statistic:

[tex]t = (\bar x - \mu) / (s / \sqrt{n} )[/tex]

When s is the sample standard deviation, n is the sample size, and x is the sample mean and is the predicted population mean.

In this case,

[tex]\bar x[/tex] = 505,

[tex]\mu[/tex] = 503,

s = 41,

n = 70.

t =  (505 - 503) / (41 / [tex]\sqrt{70}[/tex]) = 1.38

D. The P-Value:

We want to test whether the mean SAT score of the students who completed the preparation course is significantly higher than the mean score of 503 at the 0.05 level of significance.

Using a t-distribution table with 69 degrees of freedom (df = n-1), we find that the area to the right of 1.38 is 0.086.

Since this is a one-tailed test (we are testing for[tex]\mu[/tex] > 503), the P-value is 0.086.

Since the P-value (0.086) is greater than the level of significance (0.05), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the preparation course does what it claims, i.e., the mean SAT score of the students who completed the preparation course is not significantly higher than the mean score of 503.

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(x-8)²

(x-8)(x-8)

x(x-8) - 8 (x-8)

x² -8x -8x + 64

x²-16x+64

Answer: just do 30 - 13 which = 17

Step-by-step explanation:

subtraction above

Answer:

Step-by-step explanation:

a. To find the area of the sector, we can use the formula:

A = (θ/360)πr^2

where A is the area of the sector, θ is the central angle in degrees, r is the radius of the circle, and π is the constant pi.

In this case, the radius is 4 cm and the central angle is 45 degrees. Substituting these values into the formula, we get:

A = (45/360)π(4^2)

A = (1/8)π(16)

A = 2π

Therefore, the area of the sector is 2π square cm.

b. To find the area of the segment of a circle, we need to subtract the area of the triangle formed by the two radii and the chord from the area of the sector.

The central angle of the sector is 45 degrees, so the angle between the chord and one of the radii is 22.5 degrees. We can use trigonometry to find the length of the chord:

cos(22.5) = adjacent/hypotenuse

cos(22.5) = x/4

x = 4cos(22.5)

So the length of the chord is approximately 3.54 cm (rounded to two decimal places).

The area of the triangle can be found using the formula:

A = (1/2)bh

where b is the length of the base (which is the chord) and h is the height (which is the distance from the midpoint of the chord to the center of the circle). The height is equal to the radius minus half the length of the chord:

h = 4 - (3.54/2)

h = 1.23 (rounded to two decimal places)

Substituting the values of b and h, we get:

A = (1/2)(3.54)(1.23)

A = 2.17 (rounded to two decimal places)

So the area of the triangle is approximately 2.17 square cm.

Finally, we can find the area of the segment by subtracting the area of the triangle from the area of the sector:

Area of segment = Area of sector - Area of triangle

Area of segment = 2π - 2.17

Area of segment = 0.85 (rounded to two decimal places)

Therefore, the area of the segment of the circle is approximately 0.85 square cm.

The new mural dimensions are 267 inches by 273 inches.To find the new dimensions, we must add 33 inches to the original length of 234 inches, giving us a new length of 267 inches.

To calculate the new dimensions of Rhiannon's mural, we must first identify the original dimensions of the mural which are 234 inches by 245 inches. To find the new dimensions, we must add 33 inches to the original length of 234 inches, giving us a new length of 267 inches. We must also add 28 inches to the original width of 245 inches, giving us a new width of 273 inches. Therefore, the new dimensions of Rhiannon's mural are 267 inches by 273 inches.

The complete question is :

A rectangle mural measures 234 inches by 245. Rhiannon creates a new mural that is 33 inches longer. What are the dimensions of Rhiannon's new mural?

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The probability of two people on the same team having the same birthday is: P(A) = 1 / 16

The probability of two people having the same birthday in a group of 32 people is 1/365. This is because there are 365 possible days that a person can have a birthday, and the probability of two people having the same birthday is 1/365.

In this case, there are 16 teams of 2 students each, and the probability of two people on the same team having the same birthday is 1/365.

To calculate the probability of this event occurring, we can use the formula:

P(A) = n(A) / n(S)

Where P(A) is the probability of the event occurring, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.

In this case, the number of favorable outcomes is 1, since there is only one team that has two people with the same birthday. The total number of possible outcomes is 16, since there are 16 teams.

Therefore, the probability of two people on the same team having the same birthday is:

P(A) = 1 / 16

So, the probability of this event occurring is 1/16.

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Answer:

(x + 3)

Step-by-step explanation:

The required  value of the third side of the triangle is x = 11.78.

We can use the law of cosines to find the value of the third side of the triangle. The law of cosines states that for any triangle with sides a, b, and c and angle C opposite side c,

[tex]$c^2 = a^2 + b^2 - 2ab\cos(C)$[/tex]

In this case, we have sides a = 2 and b = 10 and angle C = 120 degrees. Therefore, we can plug in these values to get:

[tex]$x^2 = 3^2 + 10^2 - 2(3)(10)\cos(120^\circ)$[/tex]

Simplifying the expression inside the parentheses gives:

[tex]$\cos(120^\circ) = -\frac{1}{2}$[/tex]

Plugging this in and simplifying further gives:

[tex]$x^2 = 9 + 100 + 30 = 139$[/tex]

Taking the square root of both sides gives:

[tex]$x = \sqrt{144} = 12$[/tex][tex]$x = \sqrt{139} = 11.78$[/tex]

Therefore, the value of the third side of the triangle is x = 11.78.

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The given equation x² + 12x − 1  can be written in the form of algebraic identity (x + 6)² -37

Algebraic identities are equations in algebra that hold regardless of the value of each of their variables. The factorization of polynomials makes use of algebraic identities. On both sides of the equation, they have variables and constants.

Write x² + 12x − 1 in the form (x + a)² + b, where a and b are constants.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added to a variable before being multiplied by it.

[tex]The \ given \ equation\ is\ \\\\x^2+12x-1\\let , \ x^2+12x=1\\\\add \ both\ side \ \frac{12^2}{4}\\\\x^2+12x+\frac{144}{4}=1+\frac{144}{4}\\\\x^2+12x+36=1+36\\x^2+2.6.x+6^2-37\\\\(x-6)^2-37\\\\[/tex]

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the direct distance between the airport and Car's grandparents' house in the woods is 63.64 miles

The Pythagorean theorem is a fundamental principle in mathematics that relates to the sides of a right triangle. It is referred that the hypotenuse's square length, which is the side that faces the right angle, is equal to the sum of the squares of the lengths of the other two sides of a right triangle.

Let d be the distance between the airport and Car's grandparents' house in the woods.  Therefore, we can use the Pythagorean theorem to solve for d:

d² = 45² + 45²

d² = 2(45²)

d = sqrt(2)× 45

Therefore, the direct distance between the airport and Car's grandparents' house in the woods is approximately 63.64 miles (since sqrt(2) is approximately 1.414).

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Answer: Please correct me if I'm wrong and I will remove my answer

1:The system of linear equations can be rewritten as:

4x + y = 4 ...(1)

y = -4a + 4 ...(2)

To determine the classification of the system, we can use the method of substitution:

Substituting equation (2) into equation (1) to eliminate y:

4x + (-4a + 4) = 4

4x - 4a = 0

x - a = 0

x = a

Substituting x = a into equation (2) to find the value of y:

y = -4a + 4

So the solution of the system is (x,y) = (a, -4a+4).

Since the system has a unique solution for any value of 'a', it is a consistent independent system of equations.

2:To find the solution to the equation f(x) = g(x), we need to find the value of x that makes the two functions equal.

f(x) = 2^x + 1

g(x) = -x + 7

Setting them equal to each other:

2^x + 1 = -x + 7

Subtracting 1 from both sides:

2^x = -x + 6

Taking the logarithm of both sides (base 2):

x = log2(-x + 6)

Since log2(-x + 6) is only defined when -x + 6 is positive, we need to check if -x + 6 > 0.

-x + 6 > 0

x < 6

Therefore, the solution to the equation f(x) = g(x) is the intersection point of the two graphs for x < 6.

To graph the two functions, we can use a graphing calculator or plot points. Here are some points for each function:

f(x) = 2^x + 1

(0, 2)

(1, 3)

(2, 5)

(3, 9)

g(x) = -x + 7

(0, 7)

(1, 6)

(2, 5)

(3, 4)

Plotting these points on the same coordinate plane:

We can see that the two functions intersect at approximately (2.6, 4.4) for x < 6. Therefore, the solution to the equation f(x) = g(x) for x < 6 is approximately x = 2.6.

The measure of angle ABD as required to be determined from the task content is; 32°.

As evident in the task content;

m<ABD + m<CBD = m<ABC = 90°.

This follows from the fact that the angle ABC is a right angle.

4x - 4 + 2x + 40 = 90

6x = 54

x = 54 / 6 = 9

Ultimately, the measure of angle ABD is; 4(9) - 4 = 36 - 4 = 32.

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Singular Savings Bank received an initial deposit of $3000. By keeping a percentage of this money in reserve based on the reserve rate, the bank loaned out the rest. Over time, the money loaned out was all deposited back into the bank, and with each additional deposit the bank was able to lend out even more money.

This cycle of lending and depositing continued indefinitely until the initial $3000 had increased to $50,000. This increase in money was possible due to the reserve rate, which allowed the bank to lend out a percentage of the money deposited and to keep a percentage in reserve for themselves.

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Answer:

a= 528 squared centimeters

Step-by-step explanation:

Area of trapezoid is A=[(a+b)/2]*h

Base 1 is 32 cm

height is 12

since the height is also same as the bottom part as told by the line, do 32+12+12 to get...

56 cm for base 2

Sooo put this to use

a=[(32+56)/2]*12

a=[(88)/2]*12

a=[44]*12

a=528 :)

Answer:

Area 528cm²

That's the answer to your question.

If a store sells two types of shirts. The number of short-sleeved shirts that were sold than long-sleeved shirts is 24 shirts.

Number of short-sleeved shirts sold =S

Number of long-sleeved shirts sold = L

we know that:

s + l = 48 (equation 1) -- Total number of shirts sold

12s + 16l = 624 (equation 2) -- Total cost of shirts sold

To solve for the number of short-sleeved shirts sold, we can use equation 1 to express "l" in terms of "s":

l = 48 - s

Substituting this into equation 2

12s + 16(48 - s) = 624

Simplifying and solving for "s"

12s + 768 - 16s = 624

-4s = -144

s = 36

Therefore, 36 short-sleeved shirts were sold.

To find the number of long-sleeved shirts sold, we can use equation 1 again:

s + l = 48

36 + l = 48

l = 12

Therefore, 12 long-sleeved shirts were sold.

How many MORE short-sleeved shirts were sold than long-sleeved shirts,:

36 - 12 = 24

So, 24 MORE short-sleeved shirts were sold than long-sleeved shirts.

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The probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds is 0.0107 or 1.07%.

The probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds is 0.0013.

Given data:

Mean (μ) = 450 seconds

Standard deviation (σ) = 40 seconds

We are required to find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds.i.e., we need to find P(x < 358)

Let us first calculate the z-score.

z = (x - μ) / σ

Where,x = 358 seconds

μ = 450 seconds

σ = 40 seconds

z = (358 - 450) / 40 z = -2.3

Using a z-table or calculator, we can find the probability that corresponds to the z-score of -2.3P(z < -2.3) = 0.0107

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The amounts needed for the dessert for 16 people is given as follows:

The amounts are obtained applying the proportions in the context of the problem.

For 8 people, the amounts of the ingredients are given as follows:

With 16 people, the number of people doubles, hence the amount of ingredients also doubles, thus the needed amounts are given as follows:

Gina is preparing a recipe for 8 people, and the amounts are given as follows:

The problem asks for the necessary amounts for 16 people.

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The value of a is -9

When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on.

[tex]P(x)=4x^5+3x^2+2x+a[/tex]

Question might be asking to find the value of 'a'  at the point (1, 0) on the graph of  [tex]P(x)=4x^5+3x^2+2x+a[/tex]

Substitute the point into the polynomial.  i.e., x=1, y=0

=>  [tex]0=4(1)^5+3(1)^2+2(1)+a[/tex]

=> 0=  4*1 + 3*1+2 +a

=> 0= 4+3+2+a

=> 0=9 +a

=> a= -9

The value of a is -9

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Complete Question:

Find the value of  [tex]P(x)=4x^(5)+3x^(2)+2x+a[/tex]

Answer:

a = 24

b = 10

c = 26

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

Explanation:

We're given a list of possible b values and they are:

4, 5, 8, 10, 12, 24

Let's make a table to show what each value of 'a' would be based on those b values above.

[tex]\begin{array}{|c|c|} \cline{1-2}b & a\\\cline{1-2}4 & 12\\\cline{1-2}5 & 14\\\cline{1-2}8 & 20\\\cline{1-2}10 & 24\\\cline{1-2}12 & 28\\\cline{1-2}24 & 52\\\cline{1-2}\end{array}[/tex]

Example calculation: If b = 4, then a = 2b+4 = 2*4+4 = 12 (first row)

I recommend using spreadsheet software to quickly compute these values. Also, a spreadsheet is useful to organize the data into a table.

Next we'll add a third column c.

This column will be computed using the formula [tex]c = \sqrt{a^2+b^2}[/tex] which is based from the pythagorean theorem [tex]a^2+b^2 = c^2[/tex]

So,

[tex]\begin{array}{|c|c|c|} \cline{1-3} & & \\b & a & c = \sqrt{a^2+b^2}\\\cline{1-3}4 & 12 & 12.6491\\\cline{1-3}5 & 14 & 14.8661\\\cline{1-3}8 & 20 & 21.5407\\\cline{1-3}10 & 24 & 26\\\cline{1-3}12 & 28 & 30.4631\\\cline{1-3}24 & 52 & 57.2713\\\cline{1-3}\end{array}[/tex]

Each decimal value mentioned is approximate. The only time c is an integer is when a = 24 and b = 10.

So that's how I got a = 24, b = 10, c = 26 as the final answer.

4) Let the polynomial function of degree 4 that has roots 3, 2, 2+ i as its roots be p(x).

So, the required polynomial function is:

p(x)=(x−3)(x−2)(x−(2+i))(x−(2−i))

= (x−3)(x−2)(x^2−(2+i)x−(2−i)x+(2−i)(2+i))

= (x−3)(x−2)(x^2−2x−ix+ix+4)

= (x−3)(x−2)(x^2−2x+4)

= x^4−9x^3+28x^2−36x+24

Thus, the polynomial function of degree 4 that has real coefficients and has 3, 2 and 2+ i as some of its roots is x^4−9x^3+28x^2−36x+24.

Given: x^3−2x^2+36x−72=0 and 6i is a zero of this polynomial function.

So, we can write it as:

x^3−2x^2+36x−72= (x−6i)(x−(−6i))(x−6)

= (x−6i)(x+6i)(x−6)

As this polynomial function has real coefficients, so the imaginary roots occur in conjugate pairs.

Thus, the remaining zeros are:

−6i (as 6i is a zero, so −6i is also a zero due to conjugate pair of complex roots) and 6 (as 6i is one factor of the polynomial function, so x−6i will be its conjugate factor, which will be x+6i. And, the remaining factor will be x−6)

Therefore, the remaining zeros of x^3−2x^2+36x−72 polynomial function are −6i and 6.

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Answer:

a. 6 and 2

b. 3 and 8

Step-by-step explanation: Supplementary angles add up to 180 degrees. In this figure angles 6,2 lie on the same line and a straight line has an angle measure of 180 degrees. Vertical angles are opposite to each other and have the same value. 8 and 3 are one example and on that same area, 7 and 4 are too.

for (d), the x value has changed, as the (-1) in the series acts as a multiplier and flips the convergence of the original series. This means that when x = -4, the original series converges, but when x = -7, the series in (d) converges. Therefore, the series in (d) converges.

(a) Diverges

(b) Diverges

(c) Converges

(d) Converges: The original series converges when x = -4 and diverges when x = 6. For (a), (b), and (c), the x value remains the same as in the original series, so the convergence or divergence of the series is the same as the original series. However, for (d) the x value has changed. The (-1) in the series acts as a multiplier and flips the convergence of the original series, so the series converges.

The convergence or divergence of a series is determined by the value of x in the series. In this particular case, when x = -4 the original series converges, and when x = 6 it diverges. For (a), (b), and (c), the x value is the same as in the original series, so the convergence or divergence of the series is the same as the original series. However, for (d), the x value has changed, as the (-1) in the series acts as a multiplier and flips the convergence of the original series. This means that when x = -4, the original series converges, but when x = -7, the series in (d) converges. Therefore, the series in (d) converges.

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Answer:

I believe this what you're asking:

To estimate the sum of 3.456 and 8.79, we can round each number to one decimal place, and then add them:

3.456 ≈ 3.5

8.79 ≈ 8.8

So, 3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3

Therefore, we can estimate that the sum of 3.456 and 8.79 is approximately 12.3.

In equation form, this can be written as:

3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3

Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

Answer:

It will have a rise of 20.

Step-by-step explanation:

We can use ratios:

Rise : Run = 16 : 4 = 4 : 1 = 20 : 5

Hope this helps!

Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

The sοlutiοn tο the equatiοn is x=7.

An equatiοn is an expressiοn that uses mathematical symbοls tο express the relatiοnship between twο οr mοre variables. Equatiοns are used tο describe physical laws, mοdel real-wοrld prοblems, and sοlve mathematical prοblems. Equatiοns can be written in a variety οf fοrms, frοm simple linear equatiοns tο cοmplex nοnlinear equatiοns. Equatiοns can alsο be used tο determine the prοperties οf certain functiοns and tο evaluate integrals.

Sοlving fοr x,

−10(−x+1)+10+10(x+3)=0

−10x+10−10x+10+100+30=0

−20x+140=0

20x=140

x=7

This equatiοn is an example οf a linear equatiοn. Linear equatiοns are equatiοns that invοlve οnly οne variable and can be represented in the fοrm ax + b = 0, where x is the variable and a and b are cοnstants. Linear equatiοns are useful fοr understanding the relatiοnship between different variables and can be used tο sοlve real-wοrld prοblems. In this equatiοn, the variable x is the unknοwn value that we are trying tο sοlve fοr. By rearranging the equatiοn and applying the apprοpriate algebraic οperatiοns, we were able tο sοlve fοr x. This is an example οf hοw linear equatiοns can be used tο sοlve real-wοrld prοblems.

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Solve for x in given expression.

10 + 10(x + 3) = −x −10(−x + 1)

Answer:

25&36

Step-by-step explanation:

25 is a square number and so is 36 and there product is 900. They are also consecutive.

Just assemble the square numbers from the least i.e 4 and try solving as asked to see if it gives 900.

Thus you'll land on 25&36

Answer:

5² and 6²

Step-by-step explanation:

Use trial and error

Start from the product of 1² and 2²

1×2²

1×4=4

4<900 (incorrect)

2²×3²

4×9=36

36<900(incorrect)

3²×4²

9×16=144

144<900(incorrect)

4²×5²

16×25=400

400<900(incorrect) *but close

5²×6²

25×36 =900

900=900(correct)

: . 5² and 6² are the two consecutive square numbers.