Mathematics High School

## Answers

**Answer 1**

**Answer:**

I can tell this is your first question ;)

**Step-by-step explanation:**

Add the equations/choices next time

## Related Questions

PLEASE I WILL GIVE BRAINLIEST, 100 POINTS

### Answers

By using **parallelogram** EFGH, the proof should be completed to prove that opposite **angles **of a **parallelogram **are congruent as follows;

By the alternate interior **angles** theorem, ∠FGE ≅ ∠HEG and ∠EGH ≅ ∠GEF.

Thus, by ASA, ΔEFG ≅ ΔGHE.

By the alternate interior **angles** theorem, ∠EFH ≅ ∠GHF and ∠HFG ≅ ∠FHE.

Thus, by ASA, ΔEFH ≅ ΔGHF.

What is the Alternate Interior Angles Theorem?

In Mathematics and Geometry, the **Alternate Interior Angles** Theorem states that when two (2) parallel lines are cut through by a transversal, the **alternate interior angles** that are formed are **congruent**:

By applying the **alternate interior** **angles** theorem to **parallelogram** EFGH, we have the following:

∠FGE ≅ ∠HEG and ∠EGH ≅ ∠GEF.

ΔEFG ≅ ΔGHE (Angles, Side, Angle).

By applying the **alternate interior** **angles** theorem to **parallelogram** EFGH, we have the following:

∠EFH ≅ ∠GHF and ∠HFG ≅ ∠FHE.

ΔEFH ≅ ΔGHF (Angles, Side, Angle).

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Suppose we have a random sample X1, X2, …, Xn such that the Xi’s follow an unknown distribution with mean and variance ଶ = 25. Assuming the sample size n > 40, what is the value of n such that P(|ത − | < 1) ≅ 0.95?

### Answers

**μ_ȳ = μ**

**σ_ȳ = σ/√n**

**Here, we want to find the sample size n such that P(|ത − μ| < 1) ≅ 0.95. Using the CLT, we can write this as:**

**P(|(ȳ - μ)/(σ/√n)| < 1) ≅ 0.95**

**We can simplify this expression by multiplying both sides by σ/√n and rearranging:**

**P(|ȳ - μ| < σ/√n) ≅ 0.95**

**Now, we can use the fact that the standard deviation σ is known to substitute σ/√n with its value of 5, and we get:**

**P(|ȳ - μ| < 5/√n) ≅ 0.95**

**The absolute value of the difference |ȳ - μ| is equivalent to the distance between ȳ and μ, which is a measure of how far the sample mean is from the population mean. We want this distance to be less than 1, so we can rewrite the inequality as:**

**5/√n < 1**

**Solving for n, we get:**

**n > 25**

**Therefore, the minimum sample size required to ensure that P(|ത − μ| < 1) ≅ 0.95 is n = 26 (rounded up to the nearest integer).**

Differentiate 3x + 2/x, with respect to x. (first principle)

### Answers

The **function **3x + 2/x **differentiated** with respect to x is 3 - 2/x²

Differentiating the function 3x + 2/x, with respect to x.

From the question, we have the following parameters that can be used in our computation:

3x + 2/x

Express properly

So, we have

y = 3x + 2/x

Using the **first principle**, we have

y' = 3 - 2/x²

Hence, the **function **3x + 2/x **differentiated** with respect to x is 3 - 2/x²

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Using the image below, find the value of

csc(0) rounded to three decimal places.

X=-11

y=7

### Answers

The **trigonometric function** has the following **exact value**: csc θ = √170 / 7

How to determine the exact value of a trigonometric function

Herein we must determine the **exact value **of a **trigonometric function**, that is, the cosecant function, based on the coordinates of a vector generated by a point and the origin of the Cartesian plane. The trigonometric function is defined below:

csc θ = 1 / sin θ = 1 / [y / √(x² + y²)] = √(x² + y²) / y

Where:

θ - Direction, in degrees.x - x-Coordinate of the point. y - y-Coordinate of the point.

If we know that x = - 11 and y = 7, then the exact value of the cosecant function is:

csc θ = √[(- 11)² + 7²] / 7

csc θ = √170 / 7

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BRAINLIEST HELPPP PLEASEE FOR 20 POINTSSS!!!!!!!

A group of students were surveyed to find out if they like bike riding and/or roller skating as a hobby. The results of the survey are shown below:

80 students like bike riding

20 students like bike riding but do not like skating

90 students like skating

40 students do not like bike riding

Make a two-way table to represent the data and use the table to answer the following questions.

Part A: What percentage of the total students surveyed like both bike riding and skating? Show your work. (5 points)

Part B: What is the probability that a student who does not like bike riding also does not like skating? Explain your answer. (5 points)

### Answers

**You're trying to cheat, aren't you?**

Find the range of possible values of k such that e^2x + lnk = 3e^x has at least one real solution.

### Answers

The **range** of **possible** **values** of k such that the **function** has at least one real solution is k ≤ e^(9/4).

We have,

To find the **range** of possible **values** of k such that the **function**

e^(2x) + ln(k) = 3e^x has at least one real solution, we need to analyze the conditions for the existence of real solutions.

Let's start by rearranging the **function**:

e^(2x) - 3e^x + ln(k) = 0

Now, let's consider the **function** f(x) = e^(2x) - 3e^x + ln(k).

Taking the derivative of f(x).

f'(x) = 2e^(2x) - 3e^x

Setting f'(x) equal to zero and solving for x.

2e^(2x) - 3e^x = 0

e^x(2e^x - 3) = 0

We can see that f'(x) is equal to zero when e^x = 0 or 2e^x - 3 = 0.

However,

e^x is always positive, so the only possibility for f'(x) to be equal to zero is when 2e^x - 3 = 0.

Solving 2e^x - 3 = 0.2e^x = 3

e^x = 3/2

x = ln(3/2)

Now,

When x < ln(3/2), e^x < 1, and e^(2x) < 1.

So f(x) = e^(2x) - 3e^x + ln(k) will be negative.

When x > ln(3/2), e^x > 1, and e^(2x) > 1.

So f(x) = e^(2x) - 3e^x + ln(k) will be positive.

Therefore,

The **function** to have at least one real **solution**, we need f(x) to change the sign at x = ln(3/2).

Setting f(x) = 0.

e^(2x) - 3e^x + ln(k) = 0

The discriminant is given by:

D = (-3)^2 - 4(1)(ln(k))

For the discriminant to be non-negative, we have:

D ≥ 0

(-3)^2 - 4(1)(ln(k)) ≥ 0

9 - 4ln(k) ≥ 0

4ln(k) ≤ 9

ln(k) ≤ 9/4

k ≤ e^(9/4)

Therefore,

The **range** of **possible** **values** of k such that the **function** has at least one real solution is k ≤ e^(9/4).

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A rectangle has an area of

48

4848 square millimeters. The length of the rectangle is

8

88 millimeters. What is the width of the rectangle?

### Answers

**Answer:**

6 mm

----------------

Area of rectangle **formula**:

A = lw

We are given that A = 48 mm² and l = 8 mm.

**Substitute **these into formula **and find** the value of **w**:

48 = 8ww = 48/8w = 6

**Answer:**

6 mm

**Step-by-step explanation:**

We know that the **formula to find the area of a rectangle** is:

**Area = Length × Width**

Given that,

Length → 8 mm

Area → 48 mm²

Let us find the width of the rectangle using the formula.

Area = Length × Width

48 = 8 × w

*Divide both sides by 8 to make "w" as the subject.*

**6mm = width**

We wish to estimate the mean serum indirect bilirubin level of 4-day-old infants. The mean for a sample of 16 infants was found to be 5.98 mg/100cc. (a) What is the point estimate of the population mean for bilirubin level? (b) Assume the bilirubin levels in 4-day-old infants are approximately normally distributed with a standard deviation of 3.5 mg/100cc. Construct a 95 percent confidence interval for the population mean. State the probabilistic interpretation of the confidence interval. (c) Construct a 95% confidence interval for the population mean under the assumption that bilirubin levels in 4-day-old infants are approximately normally distributed, with mean for the sample of 16 infants was found to be 5.98 mg/100cc and standard deviation to be 2.9 mg/100cc. Compare the two confidence intervals.

### Answers

a) The point estimate of the population **mean** for bilirubin level is 5.98 mg/100cc.

b) The 95 percent confidence interval for the **population** mean bilirubin level in 4-day-old infants is (4.27, 7.69) mg/100cc.

c) The 95 percent **confidence interval** for the population mean bilirubin level in 4-day-old infants, considering the updated standard deviation, is (4.56, 7.40) mg/100cc.

(a) The point estimate of the population mean for **bilirubin** level is 5.98 mg/100cc.

(b) To construct a 95 percent confidence interval for the population mean, we can use the **formula.**

Confidence Interval = point estimate ± (critical value) * (standard deviation / √(sample size))

The critical value for a 95 percent confidence interval is 1.96 (assuming a normal distribution). The **standard deviation **given is 3.5 mg/100cc, and the sample size is 16.

Confidence Interval = 5.98 ± (1.96) * (3.5 / √(16))

Calculating the values:

Confidence Interval = 5.98 ± 1.96 * 3.5 / 4

Confidence Interval = 5.98 ± 1.96 * 0.875

Confidence Interval = 5.98 ± 1.71

Confidence Interval = (4.27, 7.69)

The 95 percent **confidence interval **for the population mean bilirubin level in 4-day-old infants is (4.27, 7.69) mg/100cc.

The **probabilistic** interpretation of this confidence interval is that if we were to repeatedly sample 4-day-old infants from the population and calculate the confidence interval each time, approximately 95 percent of the intervals would contain the true population mean bilirubin level.

(c) Using the **updated** standard deviation of 2.9 mg/100cc from the sample of 16 infants, we can calculate the confidence interval again.

Confidence Interval = 5.98 ± 1.96 * (2.9 / √(16))

Confidence Interval = 5.98 ± 1.96 * 2.9 / 4

Confidence Interval = 5.98 ± 1.96 * 0.725

Confidence Interval = 5.98 ± 1.42

Confidence Interval = (4.56, 7.40)

The 95 percent confidence interval for the **population mean** bilirubin level in 4-day-old infants, considering the updated standard deviation, is (4.56, 7.40) mg/100cc.

Comparing the two confidence intervals, we can see that the second interval is slightly **narrower** than the first one. This is due to the smaller standard deviation used in the calculation, which results in a more precise estimate of the population mean.

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1. An astronaut standing on the moon's surface throws a rock upward with an initial velocity of 50 feet per second. The height of the rock can be modeled by m = -2.7t² + 50t+ 6, where m is the height of the rock (in feet) and t is the time (in seconds). a. How high will the rock go? b. How long will it take the rock to hit the ground? C. If the astronaut throws the same rock upward with the same initial velocity on Earth, the height of the rock is modeled by e = = -16t² + 50t + 6. Would the rock hit the ground in less time on the moon or on Earth? Explain your answer.

### Answers

**Answer:**

Hope this helps and have a nice day :)

**Step-by-step explanation:**

a. To find the maximum height of the rock, we need to find the vertex of the function. The vertex occurs at t = -b/2a, where a = -2.7 and b = 50. So, t = -50 / (2*(-2.7)) = 9.26 seconds. Now we can substitute this value into the equation to find the maximum height:

m = -2.7(9.26)² + 50(9.26) + 6 = 122.2 feet

So the rock will go up to a height of 122.2 feet.

b. To find when the rock will hit the ground, we need to find the time when the height of the rock is 0. So, we can set m = 0 and solve for t:

-2.7t² + 50t + 6 = 0

Using the quadratic formula, we get:

t = (-50 ± sqrt(50² - 4*(-2.7)*6)) / (2*(-2.7))

t = 18.52 seconds or t = 0.21 seconds

Since the negative root doesn't make sense in this context, we can assume that the rock hits the ground after 18.52 seconds.

c. The time it takes for the rock to hit the ground on Earth is given by setting e = 0:

-16t² + 50t + 6 = 0

Using the quadratic formula, we get:

t = (-50 ± sqrt(50² - 4*(-16)*6)) / (2*(-16))

t = 3.71 seconds or t = 0.10 seconds

So, the rock would hit the ground much faster on Earth than on the moon. This is because the gravitational force on the moon is much weaker than on Earth, so it takes longer for objects to fall to the ground.

Which two lines represent a system of equations with solution (-6, -2)?

### Answers

The two lines that represent a** system of equations** with solution (-6, -2) are lines a and c

Which two lines represent the system of equations with solution (-6, -2)?

To find the **solution **of a **system of equations **graphically, we need to find the point where the two lines intercept.

So here we only need to see which two lines intercept at the point (-6, -2), using the given graph, we can see that the two lines that intercept at that point are the lines C and A, so the system of lines:

Line C

Line A

is the system of equations with the given solution.

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A sample of a radioactive substance decayed to 93 percent of its original amount after a year. (Round your answers to two decimal places.)

(a) What is the half-life of the substance?

(b) How long would it take the sample to decay to 10 percent of its original amount?

### Answers

The half-life of the **radioactive** substance is approximately 5.38 years and it would take approximately 15.01 years for the sample to **decay** to 10 percent of its original amount.

(a) Let's use the formula for** exponential **decay: [tex]A = A_0 * e^(-kt)[/tex], where A is the amount of the **substance** at time t,[tex]A_0[/tex] is the initial amount, k is the decay constant, and t is time. We know that after one year, [tex]A/A_0[/tex] = 0.93. We also know that after one** half-life,** [tex]A/A_0[/tex] = 0.5. So we can set up the following equation:

0.93 = [tex]0.5^(1/k)[/tex]

Taking the natural **logarithm** of both sides, we get:

ln(0.93) = (1/k) × ln(0.5)

Solving for k, we get:

k = ln(2) / (ln(0.5) - ln(0.93)) ≈ 0.129

The half-life is given by:

[tex]t_{1/2}[/tex] = ln(2) / k ≈ 5.38 years

So the half-life of the substance is approximately 5.38 years.

(b) We want to find the time t such that [tex]A/A_0[/tex] = 0.1. We can use the same formula as before, but now we know [tex]A/A_0[/tex] = 0.1 and we want to solve for t:

0.1 = [tex]e^(-kt)[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.1) = -kt

Solving for t, we get:

t = -ln(0.1) / k ≈ 15.01 years

So it would take approximately 15.01 years for the sample to decay to 10 percent of its original amount.

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Parallel lines r and s are cut by two transversals, parallel lines t and u.

Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16.

Which angles are corresponding angles with angle 8?

### Answers

**Answer:**

In the given diagram, line t is a transversal that intersects parallel lines r and s, and angle 8 is formed by the intersection of line t and parallel line s. Corresponding angles are formed when a transversal intersects two parallel lines, and they are located in corresponding (i.e., identical) positions relative to the two parallel lines.

Therefore, the corresponding angle to angle 8 would be angle 2, which is located in the same relative position as angle 8 with respect to parallel lines r and s, and transversal line t.

Find the vertex of the quadratic given the standard form:

F(x)=x2+4x-5

### Answers

(-2, -9) is the **vertex of the given** quadratic function

Vertex of a quadratic function

Given the quadratic equation below:

F(x) = x^2+4x-5

The quadratic **equation in vertex form** is expressed as:

f(x) = a(x - h)² + k

f(x) = x² + 4x - 5

f(x) = x² + 4x + 2² - 2² - 5

f(x) = x² + 4x + 4 - 4 - 5

f(x) = (x + 2)² - 9

Hence the **vertex of the function** from the resulting function is (-2, -9)

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Galena, which has a density of 0. 0074 kilograms per cubic centimeter. And tiger's eye, which has a density of 2,640 kilograms per cubic meter

### Answers

We can conclude that galena is **denser** than tiger's eye. To compare the densities of galena and tiger's eye, we need to make sure they are in the same** unit.**

The density of galena is given in** kilogram**s per cubic centimeter (kg/cm³).

The **density **of tiger's eye is given in kilograms per cubic meter (kg/m³).

We can convert the density of galena to kg/m³ by multiplying it by 1000000, since 1 m³ = 10^6 cm³:

density of galena in kg/m³ = 0.0074 kg/cm³ x 1000000 = 7400 kg/m³

Now we have both densities in kg/m³, and we can** compare** them:

The density of galena is 7400 kg/m³.

The density of tiger's eye is **2640 kg/m³.**

Therefore, we can conclude that galena is denser than tiger's eye.

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Margin of error: two percentage points; confidence level 90%; from a prior study, p is estimated by the decimal equivalent of 38%

n=

Margin of error: 0.04; confidence level 90%, p and q unknown

n=

find the critical value z a/2 that corresponds to the given confidence level.

89%

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 99% confident that his estimate is in error by no more than five percentage points question mark s?

n=

### Answers

To find the critical value for a 90% **confidence level**, we need to divide the remaining 10% of the distribution (in the tails) by 2, as we are looking for a two-tailed test. This gives us 0.05, which we can use to find the corresponding z-value using a **z-table **or calculator. The critical value z a/2 for a 90% confidence level is 1.645.

To determine the **sample** size needed to estimate the **percentage** of computers using a new operating system with a 99% confidence level and a 5% margin of error, we can use the formula [tex]n = (z^2 * p * q) / E^2[/tex]. Plugging in the values, we find that a sample size of 610 computers is needed.This sample size calculation ensures that there is a 99% chance that the true percentage of computers using the new operating system is within 5 percentage points of the estimated percentage. It also assumes that the prior estimate of 38% is **accurate**, and that the population proportion is roughly evenly split between those using the new operating system and those not using it.

It is important to note that the sample size calculation assumes a random and representative sample of computers. If the sample is not truly random or representative, the results may not be accurate. Additionally, the margin of error is affected by the sample size, so if a smaller sample is used, the margin of **error** will be larger.

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6 of 6 Sara is buying apple juice. A regular carton is 500 ml. She has 3 options. Option 1: Regular carton, 15% off the regular price Option 2: 25% more juice than regular carton, regular price Option 3: 20% more juice than regular carton, 9% off regular price Given that regular price is £1, find the cost of 1 ml of juice for each option. Give your answers to 2 dp. Determine which option is the best value and write this in the comment box. Option 1: p | Option 2: OF Р Option 3: Ор

### Answers

**Answer:**

Based on the calculations, Option 3 has the lowest price per ml of juice and is, therefore, the best value for Sara.

**Step-by-step explanation:**

To find the cost of 1 ml of juice for each option, we need to calculate the price per ml of juice.

Option 1:

Regular carton is 500 ml and costs £1, with a 15% discount, the price would be:

1 - 0.15 = 0.85

0.85 x £1 = £0.85

Price per ml of juice = £0.85 ÷ 500 ml = £0.0017/ml

Option 2:

25% more juice than the regular carton is 625 ml, which is 125 ml more than option 3. But, the price is the same as the regular carton, which means:

Price per ml of juice = £1 ÷ 625 ml = £0.0016/ml

Option 3:

20% more juice than the regular carton is 600 ml, and with a 9% discount, the price would be:

1 - 0.09 = 0.91

0.91 x £1 = £0.91

Price per ml of juice = £0.91 ÷ 600 ml = £0.0015/ml

Based on the calculations, Option 3 has the lowest price per ml of juice and is, therefore, the best value for Sara.

1. Find the perimeter and area of the triangle given these triangles. Show

complete solution.

a.

AREA AND PERIMETER OF TRIANGLES

b.

### Answers

The **perimeter **and **area **of the **triangle **are;

1. Area = 45 square units. perimeter = 30 units

2. Area = 32 square units, perimeter= 26 units

How to determine the value

To determine the value, we have that;

The formula for calculating the **area** of a **triangle** is expressed as;

A = 1/2bh

Such that ;

b is the baseh is the height

Then, for triangle 1;

Area = 1/2 × 9 ×10

Multtiply the values, we have;

Area = 45 square units

Area of a triangle 2;

Area = 1/2 × 8 × 8

Area = 32 square units

**Perimeter** of triangle 1;

= 9 + 10 + 11 = 30 units

Perimeter of triangle 2;

= 8 + 8 + 10

= 26 units

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find parameters for the margules equation that provide the best fit of ge/rt to the data, and prepare a p-x-y diagram that compares the experimental points with curves determined by the correlation.

### Answers

The Margules equation is a **thermodynamic **model used to describe the behavior of non-ideal liquid mixtures.

It is represented as ln(γ1) = A12(x2^2) + A21(x1^2), where γ1 is the activity coefficient of component 1, A12 and A21 are the **Margules parameters**, and x1 and x2 are the mole fractions of the components.

To determine the parameters A12 and A21 that provide the best fit for the data, a regression analysis can be performed. By comparing the experimental values of ge/RT (excess **Gibbs energy**) with the values calculated using the Margules equation, the parameters can be adjusted iteratively until the best fit is achieved.

Once the parameters are determined, a p-x-y diagram can be prepared. This diagram compares the experimental data points (obtained from experimental measurements) with the curves generated using the Margules equation and the calculated activity coefficients.

The x-axis represents the **mole fraction** of one component, the y-axis represents the mole fraction of the other component, and the curves show the phase equilibrium conditions.

The diagram helps visualize the behaviour of the liquid mixture and allows for a comparison between experimental and calculated data points. This aids in validating the Margules equation and assessing its accuracy in predicting the phase behaviour of the system.

Therefore, It's important to note that specific data and calculations are required to obtain the Margules parameters and prepare the p-x-y diagram. The process involves data fitting and plotting based on **experimental measurements**, and it can vary depending on the specific liquid mixture and the available data.

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a competing model to the prototype model is the exemplar model. describe the exemplar model. how is the exemplar model different from the prototype model?

### Answers

The exemplar model is a **cognitive model** that suggests that people store and categorize objects based on specific examples, or exemplars, that they have encountered in the past.

This means that when people encounter a new object, they compare it to all of the exemplars they have stored in their memory and categorize it based on the **exemplar **that is most similar to it.

Unlike the **prototype **model, which suggests that people form categories based on an abstract representation, or prototype, of the category, the exemplar model suggests that people form categories based on concrete examples that they have encountered in the past. This means that the exemplar model is more flexible than the prototype model because it can account for individual differences in how people categorize objects.

The exemplar model is a cognitive model that suggests that people store and categorize objects based on specific examples, or exemplars, that they have encountered in the past. Unlike the prototype model, which suggests that people form categories based on an **abstract **representation, or prototype, of the category, the exemplar model suggests that people form categories based on concrete examples that they have encountered in the past. This means that the exemplar model is more flexible than the prototype model because it can account for individual differences in how people categorize objects.

In summary, the exemplar model is a competing model to the prototype model that suggests that people store and categorize objects based on specific examples, or exemplars, that they have encountered in the past. The exemplar model is different from the prototype model because it suggests that people form categories based on concrete examples rather than an abstract prototype. The exemplar model is more **flexible **than the prototype model because it can account for individual differences in how people categorize objects.

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Name the gigure from by joining the co-orfinatr (3,5),(2,5),(-3,2) and (2,2)

### Answers

Yes, that is correct. The four points (3,5), (2,5), (-3,2), and (2,2) form a four-sided polygon or a **quadrilateral**. A quadrilateral is any four-sided polygon, and it can have different shapes and properties depending on the angles and sides of its vertices

The set of four points (3,5), (2,5), (-3,2), and (2,2) form a closed shape with four straight sides, known as a **polygon**. Specifically, this polygon has four sides and is therefore known as a quadrilateral.

Quadrilaterals can have different **shapes **and properties depending on the **angles **and sides of their vertices. In this case, the quadrilateral formed by these four **points **is a trapezoid.

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

The parallel sides of this **trapezoid **are formed by the line segments connecting (3,5) and (2,5), and (-3,2) and (2,2), while the non-parallel sides are formed by the line segments connecting (3,5) and (-3,2), and (-3,2) and (2,2).

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Question

The figure formed by joining the coordinates (3,5), (2,5), (-3,2), and (2,2) is a quadrilateral.

what is the length of the arc counterclockwise along the circle from point A to B

please view picture

### Answers

The **arc** **length** from **point** A to B is 1.8 cm.

We have,

To find the **arc** **length**, you multiply the fraction of the circle represented by the central angle (θ/360) by the total circumference of the circle (2πr).

So,

We will use the concept of the **arc** **length** of a **circle**.

i.e

The **arc** **length** is given by:

= 2πr x angle/360 _______(1)

Now,

We are given,

r = 28 cm

angle = 105

**Substituting** in (1).

= 2πr x angle/360

= 2πr x 105/360

= 2 x 3.14 x 105/360

= 1.832

= 1.8 cm

Thus,

The **arc** **length** from **point** A to B is 1.8 cm.

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Which of the following is the quotient of the rational expressions shown

below?

4x+1

÷

6x 3z-1

### Answers

**Answer:**

D) (12x^2 - x - 1)/(6x^2)

**Step-by-step explanation:**

to find the quotient of the given rational expressions, and the correct answer:

(4x+1)/(6) ÷ (x)/(3x-1)

To divide the two rational expressions, we can multiply the first fraction by the reciprocal of the second fraction:

(4x+1)/(6) × (3x-1)/(x)

Now, we can multiply the numerators and denominators of the resulting expression:

[(4x+1)(3x-1)] / [6x]

Expanding the numerator using the distributive property, we get:

[12x^2 - 4x + 3x - 1] / [6x]

Simplifying the numerator, we get:

[12x^2 - x - 1] / [6x]

We can further simplify the numerator by factoring it:

[12x^2 - x - 1] = (4x+1)(3x-1)

Substituting this factored form into the previous expression, we get:

[(4x+1)(3x-1)] / [6x]

= (12x^2 - x - 1) / (6x)

Therefore, the correct answer is:

D) (12x^2 - x - 1)/(6x^2)

I hope that helps! Let me know if you have any further questions.

Dee has $120 to spend. She went to the grocery store and spent $55. She then bought 3 potted flowers for $18 each at the nursery. How much money did Dee have left? Select each correct equation or set of equations that could be used to answer the question. 4.AR.1.1 $120 - $55 = N; N-(3x $18) = M $120 - $55 - (3 × $18) = M (3 x $18) - $55 - $120 = M ($120-$55)-(3x $18)= M $120+ $55 - (3 × $18) = M

### Answers

**Answer:**

**To find out how much money Dee had left after her purchases, we can use the equation: $120 - $55 - (3 × $18) = M. This equation represents the initial amount of money Dee had ($120) minus the amount she spent at the grocery store ($55) minus the cost of the three potted flowers ($18 each, so 3 × $18). By simplifying this equation, we can find the value of M, which represents the money Dee had left.**

Please help me!! I'm in the 7th grade but they giving us algebra I this hard i dont know what to do

### Answers

The expression that represents the **distance **between Toby's friend's house and the play ground is** √(2.5²-1.2²).**

What is a right angle triangle

A **triangle **is a plane shape that has three sides.

To calculate the **distance **between Tope's friend's house and the play gorund, we use** Pythagoras theorem.**

a² = b²+c²c = √(a²-b²).......................Equation 1

Where:

a = Distance between Toby's house and Toby's friend's houseb = Distance between Toby's house and the play groundc = Distance between Toby's friend's house and the play ground

From the diagram,

Given:

a = 2.5 inb = 1.2 in

Substitutute thesevalues into equation 1

c = √(2.5²-1.2²)

Hence, the right option is B. √(2.5²-1.2²)

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How can you determine how many liters of oil the prop maker should purchase for a miniature tank car built with a scale factor of 1 to 24

### Answers

The **prop maker **should** purchase** 3,166.7 liters of oil for the miniature tank car built with a scale factor of 1 to 24.

How to estimate the quantity of oil the prop maker should purchase?

To find out how many liters of oil the prop maker should purchase for a miniature tank car built with a **scale factor** of 1 to 24, we shall use the ratio of the **volumes** of the actual tank car and the miniature tank car:

Volume **ratio** = (miniature tank car volume) divided by (actual tank car volume)

Given:

Actual tank car volume = 76,000 L

Scale factor = 1:24

Miniature tank car volume = (1/24) x (actual tank car volume)

= (1/24) x 76,000 L

= 3,166.67 L

Therefore, the prop maker should purchase 3,166.7 liters of oil for the miniature tank car.

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**Question completion:**

Your Question was incomplete. Find below the full content:

A prop maker is working on a miniature tank car for a train derailment scene in which all the oil spills out of a tank car. The actual tank car can carry up to 76,000 L of oil. How many liters of oil should the prop maker purchase for a miniature tank car built with a scale factor of 1 to 24?

fourteen patients have the following lengths of stay: 2, 3, 4, 1, 4, 16, 4, 2, 1, 5, 4, 3, 6, and 1. compute the median.

### Answers

To compute the **median **of these fourteen patients' lengths of stay, we need to arrange them in ascending order first: 1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 6, 16. Then, we can find the middle value, which is 4, since there are an even number of values. Therefore, the median length of stay for these fourteen patients is 4.

The median is a measure of central tendency that represents the middle value of a dataset. In this case, we have fourteen patients' lengths of stay, which we need to arrange in **ascending order** before finding the middle value. Once we have arranged them, we can easily find the median, which is 4. This means that half of the patients stayed for less than 4 days, and half stayed for more than 4 days. The median is a useful measure when the dataset has outliers or extreme values that could affect the mean. In this case, we have one patient who stayed for 16 days, which is much longer than the other patients' lengths of stay. The median is not affected by this extreme value, making it a robust measure of central tendency.

In conclusion, the median length of stay for these fourteen patients is 4. By arranging the lengths of stay in ascending order and finding the middle value, we can determine the central tendency of this dataset. The median is a useful measure when dealing with datasets that have **outliers **or extreme values, as it is not affected by them. In this case, we have one patient who stayed for much longer than the others, but the median is still a reliable measure of the typical length of stay for these fourteen patients.

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The graph shows g(x) = x2 − 8x + 15. graph of parabola falling from the left, passing through 2 comma 3 to about 4 comma negative 1, and rising to the right, passing through 6 comma 3 What are the x-intercepts of g(x)? (0, 3) and (0, 5) (0, 4) and (0, 5) (3, 0) and (5, 0) (4, 0) and (5, 0)

### Answers

The correct answer is (3,0) and (5,0), which is not one of the given options. The closest option is (4,0) and (5,0), which is not entirely accurate in the graph of **parabola.**

To find the x-intercepts of the** **parabola represented by g(x) = x^2 - 8x + 15, we need to find the values of x for which g(x) equals zero. **Mathematically, **we can set g(x) = 0 and solve for x using the **quadratic formula **or by factoring the equation.

Using the quadratic formula, we have:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = 1, b = -8, and c = 15. Plugging these values into the quadratic formula, we get:

x = (8 ± sqrt(8^2 - 4(1)(15))) / 2(1)

x = (8 ± sqrt(16)) / 2

x = 4 ± 2

So the **x-intercepts** are (2,0) and (6,0). Note that these values match up with the points where the parabola intersects the x-axis in the graph.

Therefore, The correct answer can be obtained by solving for x as shown above or by reading the x-coordinates of the x-intercepts directly from the **graph **of the parabola.

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write a real life situation to match this fraction division: 1 3/4 divided by 3= 7/12

### Answers

**Answer:**

**Step-by-step explanation:**

** A recipe that calls for 1 and 3/4 cups of flour, but you want to make only one-third of the recipe. To determine how much flour you need, you can divide 1 and 3/4 by 3.**

**1 and 3/4 divided by 3 is equal to 7/4 divided by 3, which is the same as multiplying 7/4 by 1/3.**

**To solve this, you can convert 7/4 to an improper fraction:**

**7/4 = 1 and 3/4**

**So, 1 and 3/4 divided by 3 is equivalent to:**

**1 and 3/4 divided by 3 = (7/4) * (1/3) = 7/12**

**Therefore, you would need 7/12 cups of flour for your smaller cake recipe.**

What is the surface area of the rectangular prism?

240 m 2

312 m 2

360 m 2

600 m 2

PLEASE HELP 40 POINTS I DON'T HAVE MUCH TIME

### Answers

**Answer:**

312 m^2

**Step-by-step explanation:**

Surface Area of a prism is SA = 2B + Ph, where B is area of the base, P is perimeter (of the base), and h is height of the prism.

2B + Ph

2(6*6) + (6+6+6+6)(10)

2(36) + (24)(10)

312 m^2

the farmer had 200 chickens 25% of them died .How many chickens died.How many chickens remained alive

### Answers

**Answer:**

150 stayed alive

**Step-by-step explanation:**

25% = 0.25

200 *0.25 = 50 *(50 died)*

200 - 50 = 150

**150 chickens remained alive.**