simplify the question: √256÷2√8

The value of ∠ABD is 120 degrees if given an isosceles trapezoid ABCD with median XY

What is trapezoid ?

A trapezoid is a quadrilateral (a four-sided polygon) with at least one pair of parallel sides. The parallel sides of a trapezoid are called bases, and the non-parallel sides are called legs.

Since ABCD is an isosceles trapezoid, the length of AB is equal to the length of CD. Let's assume that AB = CD = a, and BC = d.

The length of XY is equal to half the sum of the lengths of the non-parallel sides AB and CD. Therefore, XY = (1/2)(AB+CD) = (1/2)(a+a) = a.

So, the length of the median XY is a.

Since ABCD is an isosceles trapezoid, the base angles A and D are congruent. Let's assume that m∠ABD = x.

Since XY is the median of ABCD, it bisects the legs AB and CD at M and N, respectively. Therefore, AM = MB = (AB/2) and DN = NC = (CD/2).

Since AD and BC are parallel, we have ∠AMB = ∠DNC (corresponding angles). Also, ∠AMB + ∠BMD = 180° (linear pair), so ∠BMD = 180° - ∠AMB.

Similarly, we have ∠CND + ∠DNC = 180° (linear pair), so ∠CND = 180° - ∠DNC.

Since AD and BC are parallel, we have ∠ABD + ∠BMD = 180° (co-interior angles), so ∠ABD = 180° - ∠BMD.

Similarly, we have ∠DCB + ∠CND = 180° (co-interior angles), so ∠DCB = 180° - ∠CND.

Since ABCD is an isosceles trapezoid, we have AB = CD, so AM + MC = DN + NB. Substituting the values, we get (a/2) + d = (a/2) + d. Therefore, d = d.

Now, we can use the fact that ∠BMD = ∠CND to get an equation in terms of x: x + ∠ABD = 180° - x + ∠DCB. Substituting d = d, we get x + ∠ABD = 180° - x + ∠ABD. Therefore, x = (1/2)*(180° - ∠ABD).

Since ABCD is an isosceles trapezoid, we have ∠ABC = ∠DCB. Also, we know that ∠ABD and ∠CBD are supplementary angles. Therefore, ∠ABD + ∠CBD = 180°. Substituting the value of x, we get (1/2)*(180° - ∠ABD) + ∠ABD = 180°. Simplifying, we get ∠ABD = 120°.

Therefore, The value of ∠ABD is 120 degrees if given an isosceles trapezoid ABCD with median XY

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The head circumference of a newborn boy who marks the start of the 75th percentile is approximately 35.38 cm.

To find the head circumference of a newborn boy who marks the start of the 75th percentile, we need to first find the z-score corresponding to the 75th percentile using the standard normal distribution.

The z-score formula is

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

To find the z-score that corresponds to the 75th percentile, we need to look up the z-score associated with a cumulative area of 0.75 under the standard normal distribution curve. This value can be found using a table or calculator and is approximately 0.674.

Now we can use the formula for the z-score to solve for the head circumference of a newborn boy at the 75th percentile

z = (x - μ) / σ

0.674 = (x - 34.5) / 1.3

0.674 × 1.3 = x - 34.5

0.8762 + 34.5 = x

x = 35.3762

x ≈ 35.38 cm

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Answer:more context?

Step-by-step explanation:

Step-by-step explanation:

A. To find the equation of a line parallel to line f (y = 2) and passing through point P(-2, -1), we need to understand that parallel lines have the same slope. Since line f is a horizontal line with a slope of 0, the line we are looking for will also have a slope of 0. The equation for a horizontal line with the same y-intercept as point P is simply y = -1.

B. To find the equation of a line parallel to line g (y = 2x - 1) and passing through point P(-2, -1), we need to consider that parallel lines have the same slope. The slope of line g is 2. Using the point-slope form (y - y1 = m(x - x1)), where m is the slope and (x1, y1) is the given point P(-2, -1):

y - (-1) = 2(x - (-2))

y + 1 = 2(x + 2)

Now, we can convert this to slope-intercept form (y = mx + b):

y = 2x + 4 - 1

y = 2x + 3

C. To find the equation of a line perpendicular to line f (y = 2) and passing through point Q(3, -2), we need to know that perpendicular lines have slopes that are negative reciprocals of each other. Since line f is a horizontal line with a slope of 0, the line perpendicular to it will be a vertical line. The equation for a vertical line passing through point Q with the same x-coordinate is simply x = 3.

D. To find the equation of a line perpendicular to line g (y = 2x - 1) and passing through point Q(3, -2), we need to find the negative reciprocal of the slope of line g. The slope of line g is 2, so the negative reciprocal is -1/2. Using the point-slope form (y - y1 = m(x - x1)), where m is the new slope and (x1, y1) is the given point Q(3, -2):y - (-2) = -1/2(x - 3)

y + 2 = -1/2(x - 3)

Now, we can convert this to slope-intercept form (y = mx + b):

y = -1/2x + 3/2 - 2

y = -1/2x - 1/2

The required fencing feet. for the right triangle lot, is given as 560.84.

Perimeter is the measure of the figure on its circumference. Here, the two sides of the lot is known, we have to evaluate the third side before calculating the perimeter.

Measure of the third side = √[200² + 125²]

The measure of the third side = 235.84

Now, the total fencing required = Perimeter of the triangle

= 200 + 125 + 235.84

= 560.84 ft

Thus, the required fencing for the right triangle lot is 560.84.

Full question "David must install fencing around a lot that is shaped like a right triangle. The side of the lot that runs east-west is 200 ft long. The side of the lot that runs north-south is 125 ft long."

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The easiest equation to identify the x-intercepts is the factored form of a quadratic equation, or option A.

The equation that is the easiest to identify the x-intercepts is the factored Form.

Option A is the correct answer.

We have,

In factored form, the equation is written as a product of linear factors, and the x-intercepts (or roots) are easily identifiable by setting each factor equal to zero and solving for x.

The x-intercepts correspond to the values of x when the entire expression becomes zero, which happens when at least one of the factors equals zero.

Thus,

The equation that is the easiest to identify the x-intercepts is the factored Form.

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As I became more experienced playing the game, I began to adjust my budgeting process to account for my changing needs.

Budgeting is a financial planning process that involves creating a plan to manage your income and expenses over a specific period of time.

My budgeting process involved taking the total amount of money I had to spend and splitting it up into different categories based on my needs.

I allocated a portion of the money for food, transportation, entertainment, and other expenses.

As I became more experienced playing the game, I began to adjust my budgeting process to account for my changing needs.

For example, I started to prioritize saving for a larger expense, such as a trip, over smaller items like eating out or entertainment.

I also re-evaluated my spending habits regularly to see if I could be saving money in any area or if I could be spending it more efficiently.

This process helped me to become more mindful and intentional with my spending and allowed me to make smart decisions with my money.

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Answer:1 hour 15 Minutes

Step-by-step explanation:The glider begins its flight mile above the ground.

Distance above the ground after 45 minutes =

Change in height of the glider

Next, we determine how long the entire descent last.

Expressing the distance moved as a ratio of time taken

Therefore: Total Time taken =45+30=75 Minutes

=1 hour 15 Minutes

The equations of the functions are x = -10, y = x + 5 and y = x² + 6x + 10, and the identities are shown below

Constant function

This function remains constant regardless of the input and/or output.

The graph shows a vertical line located at x = -10.

The function represented by this graph is constant, with a domain of x = -10 and a range of y [0, 12.25]

Linear function

The function varies continuously in relation to both x and y.

We can observe two points on the graph, which are (-4, 1) and (-2, 3).

From the point, we can see that y is more than x by 5

This means that the function is y = x + 5

The following identities of the functions are Domain: [-4, -2] and Range: [1, 3]

Quadratic function

This function can be represented as

y = a(x - h)² + k

From the graph, we have

(h, k) = (-3, 1) and (x, y) = (-2, 2)

By substitution, we have

y = a(x + 3)² + 1

By substitution, we have

2 = a(-2 + 3)² + 1

Solving for a, we have

a = 1

So, we have

y = (x + 3)² + 1

y = x² + 6x + 10

This means that the function is y = x² + 6x + 10 with the following identities

Domain: [-4, -2]

Range: [1. 2]

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The best ordered pair for the solution of the equations is x and y = 7.5 and 1.17 respectively

Recall that Simultaneous Equations are sets of algebraic equations that share common variables and are solved at the same time (that is, simultaneously

The given equations are

y = -1/3x + 4 and

y = 1/3x -1

This implies that

y+ x/3 = 4  ................1

y -x/3 = -1  ................11

Eliminating y we have

2x/3 = 5

This implies that 2x = 15 Making x the subject of the relation we have

x = 7.5

Put x = 7.5 in equation 1 to have

y= x/3 = 4  ................1

y +7.5/3 = 4

Collecting like terms to have

y = 4-2.83

y = 1.17

Therefore the best options are x and y = 7.50 and 1.17

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Answer: #4 = Non-Linear & #3 = Linear

Step-by-step explanation: Non-Linear lines create curves and not straight lines. As the term non-"line"ar defines not as a line, linear represent straight lines. Hence, #4 is non-linear and #3 is linear in terms of graphing.

The probability that the maximum speed of a randomly selected moped differs from the mean value by at most 1.5 standard deviations is 0.8664

We know that the maximum speed of a moped is normally distributed with mean μ = 46.8 km/h and standard deviation σ = 1.75 km/h. We want to find the probability that the maximum speed differs from the mean value by at most 1.5 standard deviations, i.e., we want to find P(|X - μ| ≤ 1.5σ), where X is the maximum speed of a moped.

Using the properties of the normal distribution, we can standardize X to get a standard normal distribution

Z = (X - μ) / σ

Substituting the values of μ and σ, we get

Z = (X - 46.8) / 1.75

We want to find P(|Z| ≤ 1.5), which is the probability that Z lies between -1.5 and 1.5.

Using a standard normal distribution table or a calculator with a normal distribution function, we can find that P(|Z| ≤ 1.5) = 0.8664.

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The given question is incomplete, the complete question is:

Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. Suppose the maximum speed of a moped is normally distributed with mean value 46.8 km/h and standard deviation 1.75 km/h. Consider randomly selecting a single such moped. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?

Answer:

2100 km

Step-by-step explanation:

If the entire trip was 2400 km, then we can note that x km was flown by plane, and 2400 - x km by bus

The whole trip took 8 hours and we know that t = s/v:

[tex]t(by \: plane) = \frac{x}{700} [/tex]

[tex]t(by \: bus) = \frac{2400 - x}{60} [/tex]

Now we can form an equation:

[tex] \frac{x}{700} + \frac{2400 - x}{60} = 8 [/tex]

[tex] \frac{60x + 1680000 - 700x}{42000} = 8[/tex]

[tex] \frac{ - 640x + 1680000}{42000} = 8 [/tex]

Use the property of the proportion:

-640x + 1680000 = 336000

-640x = 336000 - 1680000

-640 x = -1344000 / : (-640)

x = 2100

Since we've noted that x is a path flew by the plane, we have the answer already

Answer:

-4 and 4

Step-by-step explanation:

To solve this, we can take the square root of both sides, which would give us x = -4 and 4.

On the number line, you can label these points.

The p-value is   [tex]p(t < \frac{4-4.8}{\sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}})[/tex] .

What is p-value?

The P value is the likelihood, for a particular statistical model, that the statistical summary would be either equal to or more extreme than the actual observed results if the null hypothesis were to hold.

Here Average of 10 mice on old diet = 4 ounces and Standard deviation = 0.3 ounces.

Average of 10 mice on new diet = 4.8 ounces and standard deviation = 0.2 ounces.

With unknown population standard deviations, the t-distribution must be used,

[tex]\sigma_{\overline x_1-\overline x_2} = \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}[/tex]

=> [tex]\sigma_{\overline x_1-\overline x_2} = \sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}[/tex]

Now the p-value is ,

=>  [tex]p(t < \frac{4-4.8}{\sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}})[/tex]

Hence the p-value is   [tex]p(t < \frac{4-4.8}{\sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}})[/tex] .

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4. CE is a median of triangle ADF,  BF is the midpoint of AC.

5. CE = 3√3 cm and AG = 18√3 cm

6. AM is a median of right triangle ABC.

In mathematics, a triangle is a geometric shape that consists of three line segments that intersect at three endpoints. These endpoints are called vertices, and the line segments are called sides.

Triangles are one of the most basic shapes in geometry and are used in many areas of mathematics, science, engineering, and everyday life. They can be classified based on the length of their sides and the measure of their angles.

4. CE is a median of triangle ADF.

BF is the midpoint of AC.

Since C is the midpoint of segment AD and E is the midpoint of segment FD, CE is a median of triangle ADF. This is because CE passes through D and divides the opposite side A F into two equal halves.

Similarly, since B is the midpoint of segment AC, BF is a midpoint of AC. This is because BF passes through A and divides the opposite side AC into two equal halves.

5. To find CE and AG, we can use the fact that BF = 24 cm. Let's start by finding CE.

Since BF is the midpoint of AC, we have:

AC = 2 BF = 2(24 cm) = 48 cm.

Since C is the midpoint of AD, we have:

AD = 2 CD = 2 CE (by definition of midpoint)

Therefore, CE = AD/2

To find AD, we can use the fact that E is the midpoint of FD, so:

FD = 2 FE = 2 FG (by definition of midpoint)

Since F is the midpoint of GE, we have:

GE = 2 GF (by definition of midpoint)

Therefore, AG = AE + GE = AE + 2GF

Now, since AM is a median of triangle ABC, we have:

AM² = (AB² + BC²)/2 - (AC²/4)

Since triangle ABC is a right-angled triangle with angle B = 90 degrees, we have:

AB² + BC² = AC²

Therefore, we can simplify the equation for AM² as follows:

AM² = AC²/2 - AC²/4

AM² = AC²/4

Substituting the value we found for AC, we get:

AM² = 48²/4 = 576

Therefore, AM = 24 cm.

Now, we can use the Pythagorean theorem to find AE:

AE² + EM² = AM²

AE² + (AC/2)² = AM²

AE² + 24² = 576

AE² = 576 - 576/4 = 432

AE = √432 = 12√3 cm

Finally, we can find AG as:

AG = AE + 2GF = AE + 2(AD/4) (since G is the midpoint of EF)

AG = 12√3 + AD/2

But we know that AD = 2CE, so:

AG = 12√3 + CE

Therefore, to find AG, we just need to add the value of CE that we found earlier:

AG = 12√3 + CE = 12√3 + (AD/2) = 12√3 + (CE/2) = 12√3 + 6√3 = 18√3 cm.

Therefore, CE = AD/2 = (AG - 12√3)/2 = (18√3 - 12√3)/2 = 3√3 cm.

So, CE = 3√3 cm and AG = 18√3 cm.

6. Statement: AM is a median of right triangle ABC.

A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side. In right triangle ABC, the median AM joins the right angle vertex A to the midpoint of the hypotenuse BC.

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4). Section AC's midpoint is B, and section BF's midpoint is BF. Because BF cuts through A and splits the opposing side AC into two equal halves, this is the case.

5). CE = AD/2 = (AG - 12√3)/2 = (18√3 - 12√3)/2 = 3√3 cm.

So, CE = 3√3 cm and AG = 18√3 cm.

6). The middle of the hypotenuse BC is connected to the right angle vertex A by the median AM.

One of the most fundamental geometric shapes, triangles are used frequently in mathematics, science, engineering, and daily living. They can be categorized based on the dimensions of their edges and sides.

4). ADF's triangle's middle is CE.

BF sits in the middle of AC.

Triangle ADF's median is CE because C is the midway of segment AD and E is the midpoint of segment FD. This is the case because CE passes through D and divides the opposite side A F into two equal halves.

BF functions as an AC midpoint in a manner similar to how B acts as the segment's halfway point. This is the case because BF cuts through A and divides the opposite side AC into two equal halves.

5). We can use the knowledge that BF = 24 centimeters to determine CE and AG. Let's begin by locating CE.

Because BF is AC's middle, we have:

AC = 2 BF = 2(24 cm) = 48 cm.

Since C is the midpoint of AD, we have:

AD = 2 CD = 2 CE (by definition of midpoint)

Therefore, CE = AD/2

To find AD, we can use the fact that E is the midpoint of FD, so:

FD = 2 FE = 2 FG (by definition of midpoint)

Since F is the midpoint of GE, we have:

GE = 2 GF (by definition of midpoint)

Therefore, AG = AE + GE = AE + 2GF

Now that triangle ABC's middle is AM, we have:

AM² = (AB² + BC²)/2 - (AC²/4)

Triangle ABC has a right angle of 90 degrees, so we have:

AB² + BC² = AC²

As a result, we can simplify the AM² equation as follows:

AM² = AC²/2 - AC²/4

AM² = AC²/4

When we substitute the AC number we discovered, we obtain:

AM² = 48²/4 = 576

Therefore, AM = 24 cm.

We can now determine AE using the Pythagorean theorem:

AE² + EM² = AM²

AE² + (AC/2)² = AM²

AE² + 24² = 576

AE² = 576 - 576/4 = 432

AE = √432 = 12√3 cm

Finally, we can find AG as:

AG = AE + 2GF = AE + 2(AD/4) (since G is the midpoint of EF)

AG = 12√3 + AD/2

But we know that AD = 2CE, so:

AG = 12√3 + CE

The value of CE that we previously discovered can therefore simply be added to obtain AG:

AG = 12√3 + CE = 12√3 + (AD/2) = 12√3 + (CE/2) = 12√3 + 6√3 = 18√3 cm.

Therefore, CE = AD/2 = (AG - 12√3)/2 = (18√3 - 12√3)/2 = 3√3 cm.

So, CE = 3√3 cm and AG = 18√3 cm.

6). AM is the middle of the right triangle ABC.

A line section connecting a triangle's vertex to the middle of the other side is the triangle's median. The median AM connects the right angle vertex A to the middle of the hypotenuse BC in the right triangle ABC.

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The remainder when the function p(x) is divided by x + 4 as required in the task content is; -0.5.

It follows from the task content that the remainder when a function p(x) is divided by (x + 4).

However, it is important to note that the value of the function at x = -4 represents the remainder of the function when the function p(x) is divided by (x + 4).

Therefore, by checking the value of p (-4) as required, the remainder when the function p(x) is divided by x + 4 as required in the task content is; -0.5.

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In one hour, Ben would have completed 9/10 or 90% of his assignment.

Let us assume that the total assignment stands as x. Ben finished 3/5x in 2/3 of 60 minutes. 2/3 of 60 minutes is 40 minutes. So, 3/5x was finished in 40 minutes.

If 3.5x was finished in 40 minutes, in 60 minutes, Ben would have completed 90% of his assignment. This can be represented thus:

3/5x = 40 min

?       = 60 min

3/5x × 60 min/40 min

36xmin/40 min

x = 9/10

In summary, we can conclude that Ben would have completed 90% of his assignment in one hour. The same result will be obtained with visual models like the Tape diagram.

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Part A: To create a triangle: a ≤ b+c and a ≥ b−c.

Part B: Three side lengths form a triangle: A.10, 20, 15 ; B.8, 4, 12 and D.20, 10, 30.

The triangle inequality, written as a + b c, states that any two triangle sides added together must be greater than or equal to the third side a + b ≥ c. The basic tenet of the theorem is that a straight line connects any two places.

Part A: a__b+c and a __b−c.

By using the  triangle inequality,

The longest side is less than equal to the other sum of other two sides:

Thus,

a ≤ b+c and a ≥ b−c.

Part B: Three side lengths form a triangle.

A.10, 20, 15

10 + 15 ≥ 20 (longest side) (correct option.)

B.8, 4, 12

8 + 4 ≥ 12 (longest side) (correct option.)

C.8, 8,20

8 + 8 ≥ 20 (longest side) (incorrect option.)

But 16 < 20 (incorrect option.)

D.20, 10, 30

10 + 20 ≥ 30 (longest side) (correct option.)

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The compound interest on $15000  for 2 years at 6% p. a is $1956 .

To calculate the compound interest on 15000 $ for 2 years at 6% p.a., we can use the formula

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

where:

A = the final amount (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

Here, P = $15000 , r = 6% = 0.06, n = 1 (compounded annually), and t = 2 years.

So, A = 15000 (1 + 0.06/1)^(1*2)

= 15000 (1.06)^2

= $16956

Therefore, the compound interest on $15000  for 2 years at 6% p.a. is $16956 - $15000 = $1956 .

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Step-by-step explanation:

Let's use the Pythagorean Theorem to find the length of one side of the square.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the diagonal of the square is the hypotenuse of a right triangle, and the two sides are the sides of the square. Let's call the length of one side of the square "s".

Using the Pythagorean Theorem, we get:

s^2 + s^2 = 12^2

2s^2 = 144

s^2 = 72

s = √72

s ≈ 8.49

Now that we know the length of one side of the square, we can find the perimeter by multiplying by 4 (since all four sides of a square have the same length):

Perimeter = 4s

Perimeter = 4(√72)

Perimeter ≈ 33.96 cm

Therefore, the perimeter of the square with a diagonal of length 12 cm is approximately 33.96 cm.

Answer:

We can begin by finding the total surface area of the can. The area of the label is given as 66π square inches. Since the label is wrapped around the outside of the can, the area covered by it is the lateral surface area of the cylinder. The lateral surface area of a cylinder is given by 2πrh, where r is the radius and h is the height of the cylinder. We can write the equation for the lateral surface area as: 2πrh = 66π Simplifying this equation, we get: rh = 33 We also know that the radius of the can is given as 3 inches. Substituting this value in the above equation, we get: 3h = 33 Solving for h, we get: h = 11 inches Therefore, the height of the can is 11 inches.

If a father has a color blindness condition and a mother has a homozygous dominant trait for normal vision, there is a 50% probability that one of their children will inherit color blindness.

The father is color blind, which means he has only one X chromosome, and that chromosome carries the gene for color blindness. The mother is homozygous dominant for normal vision, which means she has two copies of the normal vision gene.

The offspring will inherit one X chromosome from each parent. If a son inherits the X chromosome from the mother that carries the normal vision gene, he will have normal vision because he only needs one copy of the normal vision gene to express it.

However, if a son inherits the X chromosome from the father that carries the gene for color blindness, he will be color blind because he does not have another X chromosome to compensate for the faulty gene.

Since there is a 50% chance that a son will inherit the X chromosome from the father that carries the gene for color blindness and a 50% chance that he will inherit the X chromosome from the mother that carries the normal vision gene, the probability of their offspring being color blind is 50%.

Hence, the correct answer is 50%

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Two functions that satisfy the given condition and are linearly independent on (-∞,∞) are f1(x) = e^(x) and f2(x) = e^(x)

Let's start by recalling the definition of the Wronskian for two functions f1(x) and f2(x):

W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)

Given the Wronskian W(f1,f2)(x) = e^(2x), we can try to find functions f1(x) and f2(x) that satisfy this condition. One possible solution is:

f1(x) = e^(x)

f2(x) = e^(x + C)

where C is a constant. We can now calculate the Wronskian of f1(x) and f2(x):

W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)

= e^(x) [e^(x + C)]' - [e^(x)]' e^(x + C)

= e^(x) e^(x + C) - e^(x) e^(x + C)

= 0

This means that f1(x) and f2(x) are linearly dependent. However, we can modify our choice of f2(x) by setting C= -x, which gives:

f2(x) = e^(2x - x) = e^(x)

Now we can calculate the Wronskian again:

W(f1,f2)(x) = f1(x)f2'(x) - f1'(x)f2(x)

= e^(x) [e^(x)]' - [e^(x)]' e^(x)

= e^(2x)

Since the Wronskian is non-zero, this means that f1(x) and f2(x) are linearly independent on (-∞,∞).

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The given question is incomplete, the complete question is:

Determine two functions, defined on the interval (−∞,∞), whose Wronskian is given by W(f 1 ,f 2)=e ^2x. Are the functions that you found linearly independent on (−∞,∞)

The required mean and the standard deviation of the given data based on number of tickets is equal to 111.2 and 32.84 respectively.

Calculate the mean,

Add up all the values in the set and divide by the total number of values,

Mean

= ( Sum of all the observations ) / ( Total number of observations )

= (135 + 71 + 69 + 80 + 158 + 152 + 161 + 96 + 122 + 118 + 87 + 85) / 12

= 1334 / 12

= 111.2

So the mean number of tickets sold is 111.2.

Standard deviation,

Calculate the standard deviation,

First need to calculate the variance.

The difference between each value and the mean, squaring those differences, adding them up, and dividing by the total number of values,

= ((135 - 111.2)^2 + (71 - 111.2)^2 + (69 - 111.2)^2 + (80 - 111.2)^2 + (158 - 111.2)^2 + (152 - 111.2)^2 + (161 - 111.2)^2 + (96 - 111.2)^2 + (122 - 111.2)^2 + (118 - 111.2)^2 + (87 - 111.2)^2 + (85 - 111.2)^2) / 12

= (566.44 + 1616.04 + 1780.84 + 973.44 + 2190.24 + 1664.64 + 2480.04 + 231.04 + 116.64 + 46.24 + 585.64+ 686.44) / 12

= 12937.68 /12

= 1078.14

Square root of the variance to get the standard deviation,

√1078.14= 32.84

So the standard deviation is approximately 32.84.

Therefore, the mean and the standard deviation is equal to 111.2 and 32.84 respectively.

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The above question is incomplete, the complete question is:

Susan keeps track of the number of tickets sold for each play presented at the community theater. within how many standard deviations of the mean do all the values fall?

135, 71, 69, 80, 158, 152, 161, 96, 122, 118, 87, 85.

Answer: A. Let's use x to represent the number of hours Opal works for the photographer, and y to represent the number of hours she coaches soccer. Then we can create the following system of inequalities to represent the situation:

12x + 7y ≥ 150 (Opal needs to earn at least $150 per week)

x + y ≤ 20 (Opal cannot work more than 20 hours per week)

B. There are different ways Opal can meet her goals, but here are two possible solutions:

Solution 1: Opal works for the photographer for 10 hours and coaches soccer for 10 hours. Then her total earnings for the week would be:

12(10) + 7(10) = 120 + 70 = $190

This meets her goal of earning at least $150 per week, and it also satisfies the constraint that she cannot work more than 20 hours per week.

Solution 2: Opal works for the photographer for 15 hours and coaches soccer for 5 hours. Then her total earnings for the week would be:

12(15) + 7(5) = 180 + 35 = $215

This also meets her goal of earning at least $150 per week, and it satisfies the constraint that she cannot work more than 20 hours per week.

C. To check if (10,6) is a solution to the system of inequalities, we need to substitute x = 10 and y = 6 into both inequalities and see if they are true:

12(10) + 7(6) ≥ 150

120 + 42 ≥ 150

162 ≥ 150 (true)

10 + 6 ≤ 20 (true)

Since both inequalities are true, (10,6) is a solution to the system. However, this solution does not meet Opal's goal of earning at least $150 per week, as her total earnings would be:

12(10) + 7(6) = 120 + 42 = $162

So, while (10,6) satisfies the constraints of the system, it is not a valid solution to the problem.

Step-by-step explanation:

Answer:

[tex]x=\frac{6}{5}[/tex]

Step-by-step explanation:

Solve for x:

[tex]8x+6 < 18-2x[/tex]

Add 2x to both sides

[tex]10x+6 < 18[/tex]

Subtract 6 on both sides

[tex]10x < 12[/tex]

Divide by 10

[tex]x=\frac{12}{10}[/tex]

Simplify fraction

[tex]x=\frac{6}{5}[/tex]

81 must be the bare minimum acceptable sample size for a real-world computation.

The mean of a group of two or more integers is the straightforward mathematical average. The geometric mean approach, which uses the average of a set of products, and the arithmetic mean technique, which uses the sum of the series' values, are only two of the techniques available to calculate the mean for a given set of data.

Given: For the population of healthy people, the mean IQ score is μ =100 and the standard deviation is б =14.

Significance level : 1-0.99=.01

Critical value : zₐ/2=2.576

Margin of error : E=4

Standard deviation : б =14

The following equation determines the sample size:

n=( zₐ/2×б /E)²

n=(2.576×14/4)²

n=81.288≈81

Hence, the minimum reasonable sample size for a real world calculation must be 81.

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the total number of coins in the museum's collection is:-144 + 90 + 60 + 30 + 10 + 5 = 339 coins.

What is histogram ?

A histogram is a graphical representation of the distribution of a dataset. It is commonly used in statistics to represent the frequency distribution of a set of continuous or discrete data. In a histogram, the data is divided into intervals, or bins, and the frequency of the data falling into each bin is represented by the height of a bar.

The x-axis of a histogram represents the range of values in the dataset, while the y-axis represents the frequency or count of data points falling within each bin. The bars of a histogram are usually drawn touching each other, as the data is continuous and there are no gaps between the bins.

To determine the total number of Roman coins in the museum's collection, we need to know the area under the histogram.

Since we know that 144 coins each weigh between 8 g and 17 g, we can calculate the total weight of those coins:

144 coins x ((17 g - 8 g)/2) = 144 coins x 4.5 g = 648 g

This means that the area of the rectangle representing those coins in the histogram is:

144 coins x 9 g = 1296 g

To find the total number of coins, we need to calculate the area of the remaining rectangles in the histogram. Since the width of each rectangle is 9 g, we can calculate the height of each rectangle by dividing its area by 9 g.

The second rectangle has an area of:

90 coins x 9 g = 810 g

So its height is:

810 g / 9 g = 90 coins

The third rectangle has an area of:

60 coins x 9 g = 540 g

So its height is:

540 g / 9 g = 60 coins

The fourth rectangle has an area of:

30 coins x 9 g = 270 g

So its height is:

270 g / 9 g = 30 coins

The fifth rectangle has an area of:

10 coins x 9 g = 90 g

So its height is:

90 g / 9 g = 10 coins

Finally, the sixth rectangle has an area of:

5 coins x 9 g = 45 g

So its height is:

45 g / 9 g = 5 coins

Therefore, the total number of coins in the museum's collection is:

144 + 90 + 60 + 30 + 10 + 5 = 339 coins.

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