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The mean height is 3.2 feet and thestandard deviation 0.6 feet. A… ... A forest ranger has data on the heights of a large growth ... mately what fraction of the trees should we expect to be.

The  fraction of the trees that is between 4.0 and 4.4 feet is 7%

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma}\)

x is the raw score, μ is mean and σ is standard deviation

Given that μ = 3.2, σ = 0.6, hence:

\(For\ x = 4:\\\\z=\frac{4-3.2}{0.6} =1.33\\\\\\For\ x = 4.4:\\\\z=\frac{4.4-3.2}{0.6} =2\)

From the normal distribution table, P(4 < x < 4.4) = P(1.33 < z < 2) = P(z < 2) - P(z < 1.33) = 0.9772 - 0.9082 = 7%

The  fraction of the trees that is between 4.0 and 4.4 feet is 7%

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Answer:

-4,1

Step-by-step explanation:

Answer:

-4,-1

Step-by-step explanation:

Factoring an equation is the process of finding the common factors that multiply to give the terms in the equation. It is a fundamental skill in algebra and is used to simplify equations, solve equations, and find solutions to problems.

In this example, we have factored the equation by using the distributive property in reverse. We have removed the product of (x+4)(x+2) from both sides of the equation. This is a very common method of factoring equations.

Another way to factor an equation is to use the difference of squares method. For example, x^2 - 25 = (x+5)(x-5).

A third method is to factor by grouping. For example, x^3 + 4x^2 -4x - 16 = (x^3 + 4x^2) - (4x + 16) = x(x^2 + 4x) -4(x + 4).

It's also important to note that not all equations can be factored. In some cases, you may need to use other methods such as completing the square or using the quadratic formula to solve the equation.

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An equation that relates y, the amount of yellow paint in liters, and the amount of blue paint in liters, needed to make the Green Goober's special green paint is 3y + 5b = 8x.

An equation is a mathematical statement that shows that two or more mathematical or algebraic expressions are equal or equivalent.

Mathematical expressions combine variables with constants, numbers, or values with the mathematical operands, addition, subtraction, multiplication, and division.

The yellow paint mixed with the blue paint = 3 liters

The blue paint mixed with the yellow paint = 5 liters

The quantity of the special green paint = 8 liters

Let the yellow paints = 3y

Let the blue paints = 5b

Let the special green paints = 8x

3y + 5b = 8x

Thus, the equation that represents the situation is 3y + 5b = 8x.

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Answer:

$172.75 is the amount Ahmed has

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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Answer:

\(m = \frac{ - 5 - 1}{2 - ( - 3)} = - \frac{6}{5} \)

A percentage is a way to describe a part of a whole. The percentage change in the price of the TV will be 60.2%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

As it is mentioned that the price of the tv 3 years ago was $500, while the current price of the tv is $199. Therefore, the percentage change in the price of the tv can be written as,

\(\rm Percentage\ change = \dfrac{\text{Initial value - Final value}}{Initial\ value} \times 100\%\)

\(\rm Percentage\ change = \dfrac{\$500-\$199}{\$500} \times 100= 60.2\%\)

Hence, the percentage change in the price of the TV will be 60.2%.

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The equation of a sphere with endpoints (5,0,5) and (7,4,7) is (x - 6)^2 + (y - 2)^2 + (z - 6)^2 = 13 .


To derive this equation, we can calculate the radius of the sphere. The midpoint of the diameter is (6,2,6) and the distance between the two points is:

√[(7 - 5)^2 + (4 - 0)^2 + (7 - 5)^2] = √26 = 5.1


Therefore, the equation of the sphere with radius 5.1 and midpoint (6,2,6) is:

(x - 6)^2 + (y - 2)^2 + (z - 6)^2 = 5.1^2 = 26.01.

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Answer:

9

Step-by-step explanation:

18/2 = 9

27/3 =9

63 = 9

I don't know how to explain this more

The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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Answer:

The Latin dance club needs to raise $178.50 to buy costumes. The club has already raised $35.70, so they need to raise $178.50 - $35.70 = $142.80 more. If each person raises the same amount, then each person needs to raise $142.80 / 7 = $20.40.

Therefore, the inequality that shows how much money each of the 7 club members needs to raise is:  m > $20.40

Step-by-step explanation:

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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Answer:

She spends about 12.45 on the nuts.

Step-by-step explanation:

2/3(7.50)+1/2(2.40)+1 1/4(5.00)

Answer:

4.75

Step-by-step explanation:

2 1/5= 11/5= 2.2 pounds

10.45 / 2.2 = $4.75

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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Based on the graph (see attachment), Tariq is 4 minutes after he left his house, until he got back home.

Distance can be defined as the amount of ground covered (traveled) by a physical object or body over a specific period of time, regardless of its direction, starting point or ending point.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

By critically observing the graph (see attachment) which models the time that elapses over the distance covered by Tariq, we have:

Time = 10 minutes - 6 minutes

Time = 4 minutes.

In conclusion, we can infer and logically deduce that Tariq is 4 minutes after he left his house, until he got back home.

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There is only one free variable (z), this system has infinitely many solutions. The answer is (F) Infinitely many.

Now, Let's write the system in matrix form:

|-9  12  0  -12 |

|15  -18  0  12 |

|0   8   - 6  -8 |

|2   -4   0   4|

And, [w = [72

         x    - 114

          y      18

          z] = - 20}

We want to use row operations to put the matrix into row echelon form:

-9  12 0  -12  

0  2  0  -14

0  0  -6  44

0  0  0  0

Now the matrix is in row echelon form. To solve for the variables, we can use back substitution. Starting with the last row, we see that $0z = 0$, so we don't have any information about $z$. Moving up to the third row, we have:

-6y+44z=0

Solving for y, we get:

y = 22/3z

Moving up to the second row, we have:

2x-14z=0

Solving for x, we get:

x = 7z

Finally, moving up to the first row, we have:

-9w+12x-12z=72

Substituting in our expressions for x and z, we get:

-9w+12(7z)-12z=72

Simplifying:

-9w+72z=72

Dividing by -9, we get:

w-8z=-8

So our solutions are of the form:

w  = - 8z

x      7z

y     22/3z

z     z

Since, there is only one free variable (z), this system has infinitely many solutions. The answer is (F) Infinitely many

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Answer:

47%

Step-by-step explanation:

3/4 of 5/8

3/4 • 5/8

15/32 = 0.46875 or 47%

Hicksian demand functions are:x1** = 2P₁x₂ ; x₂** = P₂²

Utility function: u(x1+x2) = .5ln(x1) + .25ln(x₂) .The Marshallian demand functions are: x1* = - and x₂* = P₂.

The indirect utility function is found by substituting Marshallian demand functions into the utility function and solving for v(P₁, P₂, Y).u(x1*,x2*) = v(P₁,P₂,Y) ⇒ u(-, P₂) = v(P₁,P₂,Y) ⇒ .5ln(-) + .25ln(P₂) = v(P₁,P₂,Y) ⇒ v(P₁,P₂,Y) = - ∞ (as ln(-) is not defined)

Thus the indirect utility function is undefined.

Minimum expenditure function can be derived from the Marshallian demand function and prices of goods:

Exp = P₁x1* + P₂x2* = P₁(-) + P₂P₂ = -P₁ + P₂²

Minimum expenditure function is thus:

Exp = P₁(-) + P₂²

Hicksian demand functions can be derived from the utility function and prices of goods:

H1(x1, P1, P2, U) = x1*H2(x2, P1, P2, U) = x2*

Hicksian demand functions are:

x1** = 2P₁x₂

x₂** = P₂²

If there are no restrictions on the amount of money the consumer can spend, the Hicksian demand functions for x1 and x2 coincide with Marshallian demand functions.

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The value of y = 12.

Given,

m ∠ABC = 40° and BD is the angle bisector of ∠ABC.

To find the value of y=?

Now, According to the figure,

For value x, (Adjacent angles)

3x - 1 = 34 - 2x

3x + 2x = 34 +1

5x = 35

x = 7

And, For value of y ,

A and C are altitude

3y +6 =  5y - 18

3y - 5y = -18 - 6

-2y = -24

y = 12

Hence, The value of y = 12.

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Answer:

68

Step-by-step explanation:

Let The first number = X

& the Second one = X + 16

Sum of these two numbers = 120

X + X + 16 = 120

2X = 120 - 16

2X = 104

X = 52

So , the first number = 52

& Second one = 52 + 16 = 68

Answer:

The numbers are 52 and 68.

Step-by-step explanation:

Let x be the first number and y be the second. The question tells us that:

1) x = y + 16

2) (x + y) / 2 = 60

2 equations, 2 unknowns. Solve the system. Plug equation 1 into equation 2:

(y + 16 + y) / 2 = 60

2y + 16 = 120

y + 8 = 60

y = 52

Now plug the value of y back into either original equation. I'll use the first:

x = 52 + 16

x = 68

The scale factor that was used to create triangle J’K’L’ is 1/3

From the graph, we have the following highlights:

KL = 3

K'L' = 1

The scale factor (k) from JKL to J'K'L is calculated as:

Scale factor = K'L'/KL

This gives

k = 1/3

Hence, the scale factor that was used to create triangle J’K’L’ is 1/3

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Answer:

73

Step-by-step explanation:

A= 2(wl+hl+hw)

A= 2(3.5×4+3×4+3×3.5)

A= 2(14+12+10.5)

A= 2(36.5)

A= 2×36.5

A= 73

Answer:

\(x_1 = -3 + 8\sqrt{2} = 8.3137\\\\x_1 = -3 - 8\sqrt{2} = -14.3137\\\)

Step-by-step explanation:

\(-3x^2-9x+357=9x\\\\\mathrm{Move}\:357\:\mathrm{to\:the\:right\:side}\\\\-3x^2-18x=-357\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\\\dfrac{-3x^2-18x}{-3}=\dfrac{-357}{-3}\\\\x^2+6x=119\)

\(\mathrm{Rewrite\:in\:the\:form}\:\left(x+a\right)^2=b\)

\(\left(x+a\right)^2=x^2+2ax+a^2\)

\(\mathrm{Rewrite\:in\:the\:form}\:x^2+2ax+a^2\\\\\mathrm{Comparing terms }2ax=6x\\\\a=3\\\\\mathrm{Add\:}a^2=3^2\mathrm{\:to\:both\:sides}\\\\x^2+6x+3^2=119+3^2\\\\\left(x+3\right)^2=128\\\\\)

\(\mathrm{Taking square roots on either side:}\\\\(x + 3) = \pm \sqrt{128}\\\\x = -3 \pm \sqrt{128}\)

\(128 = 64 \cdot 2\\\\\sqrt{128} = \sqrt{64} \cdot \sqrt{2}\\\\= 8\sqrt{2}\)

So the two roots are
\(x_1 = -3 + 8\sqrt{2} = 8.3137\\\\x_1 = -3 - 8\sqrt{2} = -14.3137\\\)

Answer:

2412.74

hope this helps

Answer:

yes i do

Step-by-step explanation:

1/4 x 12= 3

12 divided by 4 = 3

Based on the given data, the process is out of control.

To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.

For the X-bar chart:

The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:

UCL = 25 + (0.483 * 5) = 27.415

The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:

LCL = 25 - (0.483 * 5) = 22.585

For the R chart:

The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:

UCL = 2.004 * 5 = 10.020

The LCL (Lower Control Limit) for the R chart is 0.

Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.

Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.

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Answer:

38%

Step-by-step explanation:

since percent goes by 100 and there are 50 states you can double the 19 to get 38% of the states

Answer:

She has visited 38% of the states.

Step-by-step explanation:

19          x

-----  = --------

50.      100