Given that AB:BC is 4:3 and AC = 56. Find AB.
A
B

Step-by-step explanation:

Statements

Reasons

1. PQ || MN

1. Given

2. O is the midpoint of NP

2. Given

3. NO = OP

3. Definition of midpoint

4. ∠ZMO = ∠QOP

4. Alternate interior angles are congruent (corresponding angles of parallel lines)

5. ∠LNMO = ∠LPQO

5. Alternate interior angles are congruent (corresponding angles of parallel lines)

6. ΔMNO ≅ ΔPRO

6. Angle-side-angle (ASA) congruence theorem

7. AMNO ≅ AQPO

7. Corresponding parts of congruent triangles are congruent (CPCTC)

The measure of angle 6 is 38°.

What are vertically opposite angles?

Vertically opposite angles are pairs of angles formed by two intersecting lines that are opposite to each other and share the same vertex but are not adjacent angles.

When two lines intersect, they form four angles at the intersection point. The vertical opposite angles are the pairs of angles that are opposite to each other and are not adjacent angles.

We know that, if two lies are parallel and a transversal cuts the lines.

then, the angle formed are corresponding angles ad the vertically opposite angles formed will be equal.

similarly, In the give figure,

we ca see that angle 6 ad angle 38 are vertically opposites angle.

so, angle 6 = 38°

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Answer:

0 = 8

The input is a contradiction: it has no solutions.

Step-by-step explanation:

Hope it helps! =D

Answer:

it would be D!

Step-by-step explanation:

The points that are collinear are points E,H and K

Two or more points are said to be collinear, if the points are on the same line

From the figure, we have the following points

J, E, H, K, L and I

Of the 6 points, the points E, H and K are on the same line

i.e. line EK

Hence, the points that are collinear are points E,H and K

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Answer:E,H and K

Step-by-step explanation:

The median number of hours spent practicing per week during the nine consecutive weeks is the middle value when the hours are arranged in ascending order.

To find the median, we first need to arrange the recorded number of hours spent practicing per week in ascending order. Let's assume the recorded hours are as follows: 2, 3, 4, 5, 5, 6, 7, 8, 9.

There are a total of nine recorded hours. Since the number of hours is odd, the median will be the middle value. In this case, the middle value is the fifth number, which is 5. Therefore, the median number of hours spent practicing per week during the nine consecutive weeks is 5.

The median is a measure of central tendency that represents the middle value in a set of data. It is a useful measure for finding a typical value in a distribution. In this case, the median gives us an idea of the "typical" number of hours spent practicing per week during the nine-week period.

By arranging the hours in ascending order, we can easily identify the middle value as the median. In situations where there is an even number of data points, the median would be the average of the two middle values.

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Answer: rectangleular pyramid

Step-by-step explanation:

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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Answer:

idk

Step-by-step explanation:

idk just responding

for points

Answer:

120 miles

Step-by-step explanation:

If 1 inch = 20 miles, you can multiply both sides by 6 to figure out how many miles 6 inches represent.

We need to find the probability of a randomly selected bolt having thread length (a) within 1.9 SDs of its mean value, (b) farther than 2.4 SDs from its mean value, and (c) between 1 and 2 SDs from its mean value.

(a) To find the probability that the thread length of a randomly selected bolt is within 1.9 SDs of its mean value, we can use the empirical rule or the 68-95-99.7 rule. According to this rule, approximately 68% of the values fall within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. Therefore, the probability of the thread length being within 1.9 SDs of the mean is approximately (0.5 + 0.45) = 0.95 or 95%.

(b) The probability of a bolt's thread length being farther than 2.4 SDs from its mean value is the same as the probability of a value being beyond 2 SDs plus the probability of a value being beyond 3 SDs. The probability of a value being beyond 2 SDs is approximately 0.05, and the probability of a value being beyond 3 SDs is approximately 0.003. Therefore, the total probability is (0.05 + 0.003) = 0.053 or 5.3%.

(c) To find the probability of the thread length being between 1 and 2 SDs from the mean, we can subtract the probability of values beyond 2 SDs from the probability of values beyond 1 SD. Using the empirical rule, we know that the probability of a value being beyond 1 SD is approximately 0.32, and the probability of a value being beyond 2 SDs is approximately 0.05. Therefore, the probability of the thread length being between 1 and 2 SDs from the mean is approximately (0.5 - 0.32 - 0.05) = 0.13 or 13%.

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We need 1.75 litres of water to make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water

To make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water, we need to calculate how much water is needed.

We can do this by using the following formula:

Water = Diluted Squash - Squash First, we need to find out how much squash is in 2 litres of diluted squash.

Since the ratio is 1:7, we can divide 2 litres by the total number of parts (1 + 7 = 8) to find out how much squash is in 2 litres of diluted squash: Squash = 2 litres / 8 = 0.25 litres

Now we can use the formula to find out how much water is needed:

Water = 2 litres - 0.25 litres = 1.75 litres

Therefore, we need 1.75 litres of water to make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water.

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In Python, the double asterisk (**) operator is used for exponentiation or raising a number to a power.

When you write 5 ** 2, it means "5 raised to the power of 2", which is equivalent to 5 multiplied by itself.

The base number is 5, and the exponent is 2.

The double asterisk operator (**) indicates exponentiation.

The number 5 is multiplied by itself 2 times: 5 * 5.

The result of the expression is 25.

So, 5 ** 2 evaluates to 25.

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Answer: The first or the second point (- 2, - 3) or (- 2, 1)

Step-by-step explanation:

Ok, a relation (x, y) is a function only if, for each value x in the domain, we have only one value y in the range such that:

f(x) = y.

Here we have the pairs:

(- 2, - 3), (- 2, 1), (- 4, 3), (0, 4), (1, 1), and (2, 3).

Here, for the value x = -2, we have two different values of y.

y = 1 and y = 3.

So this is not a function, then if we want that this relation becomes a function, we must remove the first or the second point.

Answer:

I think B

Step-by-step explanation:

The proportion of students who scored higher than Willa is 0.7389. Hence, Option B is correct.

The given information is:

Mean (μ) = 78, Standard deviation (σ) = 5, and Willa scores = 74.8

The formula for the Z-score is:

Z = (x-μ) / σ

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

Substitute the values in the above formula, we get:

Z = (74.8 - 78) / 5

= -0.64

The negative sign indicates that Willa's score is less than the mean score.

Now, find the proportion of students who scored higher than Willa.

It can be done in two steps as shown below:

Step 1: Find the area under the standard normal distribution curve corresponding to the calculated Z-score.

The Z-table gives the area to the left of Z = -0.64.

The area to the right of Z is 1 - area to the left of Z.= 1 - 0.2611

= 0.7389

Therefore, the proportion of students who scored higher than Willa is 0.7389.

Hence, Option B is correct.

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Answer:

The slopes of both are m=6

Length of AB=6.082

Length of the image: 3.5 * 6.082 = 21.287

Answer:

Step-by-step explanation:

Answer:

The fraction of the beads that are red is

Step-by-step explanation:

Algebraic Expressions

A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:

r:y = 2:3

y:b = 5:4

We are required to find r:s, where s is the total of beads in the bag, or

s = r + y + b

Thus, we need to calculate:

\(\displaystyle \frac{r}{r+y+b} \qquad\qquad [1]\)

Knowing that:

\(\displaystyle \frac{r}{y}=\frac{2}{3} \qquad\qquad [2]\)

\(\displaystyle \frac{y}{b}=\frac{5}{4}\)

Multiplying the equations above:

\(\displaystyle \frac{r}{y}\frac{y}{b}=\frac{2}{3}\frac{5}{4}\)

Simplifying:

\(\displaystyle \frac{r}{b}=\frac{5}{6} \qquad\qquad [3]\)

Dividing [1] by r:

\(\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+y/r+b/r}\)

Substituting from [2] and [3]:

\(\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+3/2+6/5}\)

Operating:

\(\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{\frac{10+3*5+6*2}{10}}\)

\(\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{10+15+12}\)

\(\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{37}\)

The fraction of the beads that are red is \(\mathbf{\frac{10}{37}}\)

a. The value of C ≈ 192.5396 and k ≈ -0.002239

b. The demand function for this product is:

\(p = 192.5396e^{-0.0022394x}\)  x is approximately 427 units.

To solve for C and k, we need to use the information given in the problem to form two equations and then solve for the two unknowns.

From the first set of data, we have:

\(p = ce^ke\)

\(50 = ce^k(900)\)

From the second set of data, we have:

\(p = ce^ke\)

\(40 = ce^k(1200)\)

To solve for C and k, we can divide the second equation by the first equation to eliminate C:

\(40/50 = (ce^k(1200))/(ce^k(900))\)

\(0.8 = e^k(1200-900)\)

\(0.8 = e^(300k)\)

Taking the natural logarithm of both sides, we get:

ln(0.8) = 300k

k = ln(0.8)/300

k ≈ -0.0022394

Substituting k into one of the original equations, we can solve for C:

\(50 = ce^(k{900})\)

\(50 = Ce^{-0.0022394900}\)

\(C = 50/(e^{-0.0022394900} )\)

C ≈ 192.5396

Therefore, the demand function for this product is:

\(p = 192.5396e^{-0.0022394x}\)

To find the values of x and p that will maximize the revenue, we need to first write the revenue function in terms of x:

Revenue = price * quantity sold

\(R(x) = px = 192.5396e^{-0.0022394x} * x\)

To find the maximum of this function, we can take its derivative with respect to x and set it equal to zero:

\(R'(x) = -0.0022396x^2 + 192.5396x e^{-0.0022394x} = 0\)

Unfortunately, this equation does not have an algebraic solution.

We will need to use numerical methods to approximate the solution.

One way to do this is to use a graphing calculator or a computer program to graph the function and find the x-value where the function reaches its maximum.

Using this method, we find that the maximum revenue occurs when x is approximately 427 units, and the corresponding price is approximately $71.43.

Therefore, to maximize revenue, the small business should sell approximately 427 units of this product at a price of $71.43 per unit.

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The final expression 2|x+3| shows a vertical compression by 2 units and a horizontal translation to the left by 3units

Transformation is a means of changing the size and shape of an object in a xy-plane.

For the given function, its parent function is f(x) = |x|

The expression f(x) = 2|x| shows that the function is vertically stretched by 2 units.

The final expression 2|x+3| shows a vertical compression by 2 units and a horizontal translation to the left by 3units

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Explanation:

All three angles must add to 180. This is true for any triangle.

x+x+110 = 180

2x+110 = 180

2x = 180-110 ... subtract 110 from both sides

2x = 70

x = 70/2 .... divide both sides by 2

x = 35

As a check: 35+35+110 = 180 which helps confirm the answer.

Answer:

Step-by-step explanation:

x + x + 110 = 180 degree (sum of interior angles of a triangle)

2x + 110 = 180

2x = 180 - 110

x = 70/2

x = 35 degree

The slope is 9/5, this means that for each change in degree  in the Celsius scale there is a change of 9/5 degree in the Fahrenheit scale.

The y intercept is 32, this means that a temperature of 0 °C corresponds to 32 °F

A linear equation is given by:

y = mx + b

where y, x are variables, m is the slope of the graph and b is the y intercept.

Let F represent the temperature in Fahrenheit and C represent the temperature in Celsius.

50 °F corresponds to 10 °C it is given as (10, 50), while 212 °F corresponds to 100 °C, it is given as (100, 212). Hence:

\(F-F_1=\frac{F_2-F_1}{C_2-C_1} (C-C_1)\\\\\\F-50=\frac{212-50}{100-10}(C-10) \\\\\\F-50=\frac{9}{5}(C-10) \\\\\\F=\frac{9}{5}C+32\)

The slope is 9/5, this means that for each change in degree  in the Celsius scale there is a change of 9/5 degree in the Fahrenheit scale.

The y intercept is 32, this means that a temperature of 0 °C corresponds to 32 °F

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Answer:

9

Step-by-step explanation:

because thats the answer i just did the quiz

have a good day

The solution to the quadratic equation (x+2)2=a if one of the solution is 1 is 9

Given the quadratic equation

(x+2)^2=a

If one of the solution is 1, then x = 1

substitute

(1 + 2)^2 = a

3^2 = a

a = 9

Hence the solution to the quadratic equation (x+2)2=a if one of the solution is 1 is 9

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Answer:

the answer is 175

Step-by-step explanation:

have a good day

Answer:

The correct answer is 175.

Step-by-step explanation:

  \(13 * 20 - 15 * 9 + 20 * 7 - 6 * 15\\\)

= \(260 - 135 + 140 - 90\)

= \(400 - 225\)

= 175.

An equation to describe the relationship between g, the number of gems, and c, the number of chests is; g = 300c

In adventure A, when number of gems is 600, we see that number of chests is 2. Thus;

Rate of gems per chests = 600/2 = 300 g/c

In adventure B, when number of gems is 1500, we see that number of chests is 5. Thus;

Rate of gems per chests = 1500/5 = 300 g/c

In adventure C, when number of gems is 4800, we see that number of chests is 16. Thus;

Rate of gems per chests = 4800/16 = 300 g/c

Thus;

There is a constant rate and we can say that the equation that shows the relationship between the two variables is;

g = 300c

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Complete question is;

Lulu the Lucky puts chests of gems into her treasure vault. Each chest holds the same number of gems. The table below shows the number of gems Lulu received from three different adventures and the number of chests she needed to hold the gems.

                      Number of gems(g)     Number of chests(c)

Adventure A    600                            2

Adventure B    1500                           5

Adventure C    4800                          16

Write an equation to describe the relationship between g, the number of gems, and c, the number of chests.

Answer:

5832

Step-by-step explanation:

54+27=81x72=5832

You are pushing a 40.0 kg crate across the floor. what force is needed to start the box moving from rest if the coefficient of static friction is 0.288?

The force needed to start the box moving from rest if the coefficient of static friction is 0.288 is 112.9 N.

Force is defined as an influence that causes an object to undergo a change in motion. Static friction: Static friction is a type of friction that must be overcome to start an object moving. The force needed to start the box moving from rest can be determined using the formula below:

Force of friction = Coefficient of friction × Normal force where: Coefficient of friction = 0.288

Normal force = Weight = mass × gravity (g) = 40.0 kg × 9.8 m/s² = 392 N

Force of friction = 0.288 × 392 N = 112.896 N (approx)

The force of friction is 112.896 N (approx) and since the crate is at rest, the force needed to start the box moving from rest is equal to the force of friction.

Force needed to start the box moving from rest = 112.896 N (approx) ≈ 112.9 N (rounded to one decimal place)

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The best option for Declan's family to shop for fresh groceries would be B. Shopping at multiple stores for several items.

Ideally speaking, it would be best if Declan's family could be able to shop in a single store and be able to save up on transportation costs.

However, it is said that the  several competitive grocery stores are all close to each other and within a couple mile's radius. This means that it would be best for Declan's family to go to different stores because they would be able to take advantage of buying goods that are cheaper depending on the store.

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The interpretation of the 1001 measurements in the third set of data vary due to reasons are as follow,

Measurement error, Random variation and Sampling error.

Measurement error: The measurand being measured may have inherent variability, but measurement error can also contribute to variation in the data set.

Random variation: Even if the same measurand is being measured under the same conditions, there may be random fluctuations in the system or the environment that can cause variation in the data.

Sampling error: If the 11 measurements were not taken at random from the population of interest, then the variation could be due to sampling error.

For the 1001 measurements in the second and third data sets, some possible explanations for the variation could be measurement error, systematic variation, changes in the measurand and Sampling error.

Thus, variation in data can have many different causes, and it is important to carefully consider the context and specific factors that may be contributing to the variation when interpreting the results.

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Answer:

See below

Step-by-step explanation:

m = k/m     sub in the values given

-4 = k / 17

k = -68

so    m = -68/n     NOTE: this can also be written as  n = -68/m

Answer:

Step-by-step explanation:

Nikki,  they wrote the problem in a format that is general

y = k/ x      for the given variables  m and n  then

m = k / n   where k is some constant ( konstant)

plug in the given numbers for m and n

-4 =k / 17

solve for k

-4 * 17 = k

-68 = k

now we have a better formula

m = -68 / n  ( this is your answer a )

now plug in -136 for m

-136 = -68 / n  

solve for n

n = -68 / -136

n = 1/2   ( this is your answer b)

Hope that helps,  can you see how I did that?

Answer:

(3(3) × 3(4) ) ÷ 3(2)

(9 × 12) ÷ 6

108 ÷ 6

18

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

Answer:

∠ 3 = 60°

Step-by-step explanation:

∠ 1 and ∠ 2 are same- side interior angles and sum to 180° , then

4x + 36 + 3x - 3 = 180

7x + 33 = 180 ( subtract 33 from both sides )

7x = 147 ( divide both sides by 7 )

x = 21

Then

∠ 2 = 3x - 3 = 3(21) - 3 = 63 - 3 = 60°

∠ 2 and ∠ 3 are alternate angles and are congruent, so

∠ 3 = 60°

Answer:

60°

3(21)- 3 = 60

Step-by-step explanation:

4x+36 + 3x-3 = 180

x = 21