Find $m\angle LKM$ .

The boat travels at  18 miles per hour.

What is speed?

Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed.

The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.

Given:  A boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. The current is 3 miles per hour.

From the above information we can write,

Let, u is the boat speed in still water, then

\(\frac{30}{u-3} = \frac{42}{u+3}\)

Taking cross multiplication,

30(u + 3) = 42(u - 3)

Solving,

30u + 90 = 42u - 126

42u - 30u -126 -90 = 0

12u = 216

u = 18

Therefore, the speed of boat in still water is, 18 miles per hour.

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a. The confidence interval for the mean head circumference of all infants is from 33.3 cm to 35.5 cm.

b. The margin of error is 1.1 cm.  

c.  In this context, the margin of error represents the precision of our estimate of the true population mean.

a) To find the 90% confidence interval for the mean head circumference of all infants, we can use the formula:

CI = x ± z*(σ/√n)

Where x is the sample mean, σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired level of confidence (90% in this case).

Substituting the given values, we get:

CI = 34.4 ± 1.833*(2.1/√12)

CI = 34.4 ± 1.131

The confidence interval for the mean head circumference of all infants is from 33.3 cm to 35.5 cm.

b) The margin of error (E) is the amount added to and subtracted from the sample mean to obtain the lower and upper limits of the confidence interval, respectively.

In other words, it represents the range of values within which we can expect the true population mean to fall with a certain level of confidence.

To obtain the margin of error, we can use the formula:

E = z*(σ/√n)

Substituting the given values, we get:

E = 1.833*(2.1/√12)

E = 1.131

The margin of error is 1.1 cm.

c) In this context, the margin of error represents the precision of our estimate of the true population mean. It tells us how much the sample mean is likely to vary from the true population mean due to sampling variability.

A smaller margin of error indicates greater precision and a more accurate estimate.

For example, if we had obtained a smaller margin of error in this case, say 0.5 cm, it would mean that we can be more confident that the true population mean falls within a narrower range of values.

On the other hand, a larger margin of error, say 2.0 cm, would mean that our estimate is less precise and the true population mean could be further away from our estimate.

Therefore, the margin of error is an important measure of the reliability and validity of our estimate and should always be reported along with the confidence interval.

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The best description of the relationship between the y-axis and the line connecting F to F' after reflection over the y-axis is that they are perpendicular to each other.

When a triangle is reflected over the y-axis, its vertices swap their x-coordinates while keeping their y-coordinates the same. Let's consider the points F and F' on the reflected triangle.

The line connecting F to F' is the vertical line on the y-axis because the reflection over the y-axis does not change the y-coordinate. The y-axis itself is also a vertical line.

Since both the line connecting F to F' and the y-axis are vertical lines, they are perpendicular to each other. This is because perpendicular lines have slopes that are negative reciprocals of each other, and vertical lines have undefined slopes.

Therefore, the best description of the relationship between the y-axis and the line connecting F to F' after reflection over the y-axis is that they are perpendicular to each other.

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Step-by-step explanation:

Given:

Work = 40 Bushels of Apples

Time of Nicole = 15 Hours

Time of Carlos = 11 Hours

Unknown:

N = Nicole's Rate

C = Carlos' Rate

Equation:

W = r * t

Solution:

First, get Nicole's Rate

40 = N * 15

N = 40 / 15

Second, get Carlos' Rate

40 = C * 11

C = 40/11

Then, get the time

40 = ( N + C ) * t

40 = ( 40/15 + 40/11 ) * t

40 = 208/33 t

40 / (208/33) = t

t = 165 / 26 or 6.3462 Hours

Statement:

Therefore, it would take them approxmately 6.35 hours if they worked together.

The region common to both the cylinder x^2 + y^2 = 4 and the ellipsoid 4x^2 + 4y^2 + z^2 = 64 is an ellipse centered at the origin in the xy-plane.

The given cylinder x^2 + y^2 = 4 represents a circular cross-section in the xy-plane with radius 2. The equation of the ellipsoid 4x^2 + 4y^2 + z^2 = 64 describes a three-dimensional surface centered at the origin, with its major axes along the x, y, and z directions. By intersecting the cylinder and the ellipsoid, we find the common region between them.

To determine the intersection, we substitute x^2 + y^2 = 4 into the equation of the ellipsoid. This gives us 4(4) + z^2 = 64, which simplifies to z^2 = 48 and z = ±√48. However, since we are looking for the region inside both surfaces, we take z = -√48.

Thus, the common region lies in the xy-plane (z = 0) and is given by the equation x^2 + y^2 = 4. This equation represents an ellipse centered at the origin, with its major axis along the x-axis and a radius of 2. Therefore, the region common to both the cylinder and the ellipsoid is an ellipse centered at the origin in the xy-plane.

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The range of the function graphed above include the following: D. -∞ ≤ y ≤ 2.

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:

Range = {-∞, 2} or -∞ ≤ y ≤ 2.

Domain = {-1, ∞} or -1 < x < ∞.

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Answer:

-2

Step-by-step explanation:

f(x) + g(x) = x^2 - 2x +6x +4 = x^2 + 4x + 4

(f+g)(x)=0

x^2 + 4x + 4 = 0

x= -2

Answer:

rewrite: (x-10)^2=81

solution: x=10±9

Step-by-step explanation:

took the quiz.

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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The consumer surplus for the given demand functions and sales levels is $180, $1,900, and 1, respectively.

To find the consumer surplus for the given demand function ρ = 1450 - 0.4q and a sales level of 750, we need to integrate the demand function from 0 to the given sales level. The consumer surplus is given by the formula: CS = ∫[0 to 750] (ρ - p) dq. Evaluating the integral, we get the consumer surplus as $180.

For the demand function p = 760 - 0.2η - 0.0004\(q^2\)and a sales level of 2,900, we follow the same process. Integrating the demand function from 0 to 2,900 and evaluating the integral, we find the consumer surplus to be $1,900.

For the demand function p = 17,000\(e^{-0.020η}\) and a sales level of 43, the consumer surplus is calculated in a similar way. Integrating the demand function from 0 to 43 and rounding the result to the nearest integer, we obtain a consumer surplus of 1.

In summary, the consumer surplus for the given demand functions and sales levels is $180, $1,900, and 1, respectively.

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The smallest non-negative number congruent to 67 (mod 15) is 7.

When 67 is divided by 15, the quotient is 4 and the remainder is 7. Since we are looking for the smallest non-negative number, we consider the remainder 7 as the result.

Therefore, the smallest non-negative number congruent to 67 (mod 15) is 7.

In modular arithmetic, when we say that a number is congruent to another number modulo some modulus, it means that both numbers leave the same remainder when divided by that modulus.

In this case, 67 and 7 have the same remainder when divided by 15, so they are congruent modulo 15.

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Answer:

\(\boxed{4 units}\)

Step-by-step explanation:

Hey there!

Well if the base is 4 and we use the formula,

b*h / 2

4*4 = 16

16/2 = 8

So x is 4.

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is given by

base × height

\( A = \frac{1}{2} base × height\)

From the question

Area = 4 units²

height = 4 units

let x represent the base

We have

\(4 = \frac{1}{2} \times x \times 4\)

4 = 2x

Divide both sides by 2

Hope this helps you

The subject with the maximum average is Mathematics, while the subject with the minimum average is Social studies; moreover, there is a difference of 6 between Hindi and English.

Based on the graph and the values given about each subject, it can be concluded that the subject with the maximum average is Mathematics which has an average of 91, while the subject with the minimum average is social studies with an average of 55.

English average: 62

Hindi average: 56

62 - 56 = 6

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15?

Step-by-step explanation:

Answer:

the length of the radius of the circle = 15.

Step-by-step explanation:

The probability of getting a diamond or a king from a standard 52-card deck is 4/13.

In mathematics, probability is a measure of the likelihood that an event will occur. It is a way to quantify the chances of different outcomes or events in a random experiment or process. Probability is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event

In a standard deck of 52 cards, there are 13 diamonds and 4 kings. However, the king of diamonds is also a diamond, so we must subtract one from the total count to avoid double-counting.

So there are 13 + 4 - 1 = 16 cards that are either diamonds or kings.

The probability of picking a diamond or a king is therefore 16/52.

Simplifying the fraction, we get:

16/52 = 4/13

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Answer:

I am assuming the 8:15 was a typo and was actually supposed to be a 8:14. Anyways, they are equivalent because they all make 4:7 when simplified.

Step-by-step explanation:

4:7 = itself at this point, as they don't have numbers that can simplify each other on both sides, unless you are looking for a decimal answer.

8:14 = 4:7 <- You can divide the 8 and 14 by two. 8 divided by 2 is four, and 14 divided by 2 is 7.

16:28 = 4:7 <- You can divide the 16 and the 28 by four. 16 divided by 4 is 4, and 28 divided by 4 is 7.

20:35 = 4:7 <- You can divide both sides by 5. 20 divided by 5 is 4, and 35 divided by 5 is 7.

Answer:

A. 3/2

Step-by-step explanation:

rise/run

from (0,1) to (2,4) the y will rise 3 and the x will go right by 2

huh Step-by-step explanation:

Answer:

false

Step-by-step explanation:

a parallelogram is defined as a four sided figure with opposite sides parallel. This could include many shapes such as rectangles, so it's not ONLY rhombi.

all rhombuses are parallelograms, but not all parallelograms are rhombuses, so no ! ♡

The SSS Similarity Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are similar. This theorem is also known as the Side-Side-Side Similarity Theorem or the SSS Similarity Postulate.

What is the similarity theorem of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle similarity is indicated here by the symbol (~).

SSS or Side-Side-Side Similarity.
If all three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
From this result, we can conclude that-
∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
Hence, we have described the SSS similarity theorem.

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Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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The monthly payment added to your mortgage for property taxes is $270.25.It is important to budget for property taxes when purchasing a home, as they can be a significant expense. By applying for homestead exemption and taking advantage of other available exemptions, you can reduce your property tax burden and save money in the long run.

To calculate the monthly payment added to your mortgage for property taxes, we need to first find the taxable value of your home.

The taxable value is the appraised value minus any applicable exemptions. In this case, your home's taxable value is $315,000 - $50,000 = $265,000.

Next, we need to find the annual property tax amount. To do this, we multiply the taxable value by the tax rate of 1.22%:

Annual property tax = $265,000 x 0.0122 = $3,243

Finally, we can calculate the monthly property tax payment by dividing the annual property tax by 12:

Monthly property tax payment = $3,243 / 12 = $270.25.

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Answer:

What is it, you need help with?

Step-by-step explanation:

:)

Answer:

x - 10

Step-by-step explanation:

The original volume is x, and 10 is removed.

In mathematical terms, this is expressed as x - 10.

Answer:

88 would be the answer maybe.....

Answer:

88

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

just add x values and numbers

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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