Bayshore College staff are planning an end of the year meeting between students, parents and staff. They are to seat 5 parents, 5 students and 1 teacher in a circular arrangement around a table. In how many ways can this be done if no student is to sit next to another student and no parent is to sit next to another parent? (b) (4 pt) There are 20 student representatives who are already seated in a row of 20 seats. Out of the 20 representatives, 6 are to be chosen to give a speech. How many choices are there if no two of the chosen representatives occupy neighbouring seats?

Answers

Answer 1

The total number of choices for selecting 6 representatives without any two occupying neighboring seats is 77597520 .

(a) The number of ways to arrange 5 parents, 5 students, and 1 teacher in a circular arrangement around a table such that no student sits next to another student and no parent sits next to another parent, we can use the principle of inclusion-exclusion.

First, let's consider the arrangements without any restrictions. We have a total of 11 people to arrange around the table (5 parents + 5 students + 1 teacher), which can be done in (11 - 1)! = 10! ways.

Now, let's consider the arrangements where at least two students sit next to each other. We can treat the two adjacent students as a single entity, resulting in 10 entities to arrange around the table (4 parents + 5 student pairs + 1 teacher). This can be done in (10 - 1)! = 9! ways. However, within each student pair, the students can be arranged in 2! ways. Therefore, the total number of arrangements with at least two students sitting next to each other is 9! × 2! ways.

Similarly, we consider the arrangements where at least two parents sit next to each other. Again, we treat the two adjacent parents as a single entity, resulting in 10 entities to arrange around the table (4 parent pairs + 5 students + 1 teacher). This can be done in (10 - 1)! = 9! ways. Within each parent pair, the parents can be arranged in 2! ways. Therefore, the total number of arrangements with at least two parents sitting next to each other is 9! × 2! ways.

By the principle of inclusion-exclusion, the number of valid arrangements is given by

Valid arrangements = Total arrangements - Arrangements with at least two students sitting next to each other - Arrangements with at least two parents sitting next to each other

Valid arrangements = 10! - 9! × 2! - 9! × 2!

Valid arrangements = 2177280

(b) The number of choices for selecting 6 representatives out of 20, where no two chosen representatives occupy neighboring seats, we need to use a combination of counting techniques.

First, choose 6 seats out of the 20 seats in which the representatives will be seated. This can be done in C(20, 6) ways.

Now, since no two chosen representatives can occupy neighboring seats, we can think of the remaining 14 seats as dividers between the chosen representatives. We need to place these dividers in such a way that each chosen representative occupies a separate section.

To ensure that no two representatives occupy neighboring seats, we need to place the dividers such that each section contains at least one seat. We have 6 chosen representatives, so we need to place 5 dividers among the 14 remaining seats. This can be done in C(14, 5) ways.

Therefore, the total number of choices for selecting 6 representatives without any two occupying neighboring seats is given by:

Total choices = C(20, 6) × C(14, 5)

Total choices =  38760 × 2002

Total choices = 77597520

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Related Questions

PLZZ ILL GIVE BRAINLIESTTT

Answers

Answer:

give me poi tasjnsaklaalwkdbfbdjwo

Suppose that the volume of a triangular based pyramid is 316 cm3. If a prism has the same height and the same triangular base as the pyramid, what is the volume of the prism? Round your answer to one decimal place if needed.

Answers

Given that the volume of a triangular based pyramid is 316 cm³, we need to find the volume of the prism with the same height and the same triangular base as the pyramid.

Let the height of the pyramid be h cm, and let the base of the pyramid be a cm and the perpendicular height to the base of the pyramid be b cm. '

1. Volume of the pyramid: The volume of a triangular-based pyramid is given by the formula V = 1/3abhGiven V = 316 cm³, a = 7 cm and b = 12 cm, we have; 316 = 1/3 × 7 × 12 × h => h = (316 × 3) / (7 × 12) => h = 9 cm

2. Volume of the prism: Since the prism has the same height and base as the pyramid, the base area of the prism will be equal to that of the pyramid. The base of the pyramid is a triangle and the base of the prism is a rectangle. Let the length of the rectangular base be L cm.

Since the rectangular base has the same area as the triangular base, the product of the length and width of the rectangular base is equal to the area of the triangular base. Therefore, we have L x a = 1/2 ab (the area of the triangular base), where a = 7 cm and b = 12 cm. L = 1/2 b = 1/2 × 12 = 6 cm

The volume of the prism is given by the formula V = La h = 6 × 9 = 54 cm³

Therefore, the volume of the prism is 54 cm³.

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Chad earns $4 each day walking his neighbor's dog. He spends $8 purchasing dog treats
for the dog. Owen spends $3 each day at the local coffee shop. He has $13 saved from a
birthday gift. How many days until the boys have an equal amount of money?

Answers

3 days they with both have 4 dollars

Which of the following is true?
Group of answer choices
(LF – LS) > (EF – ES)
Slack = (LF – LS)
(LS – ES) >= 0

Answers

The statement that is true is (LS – ES) >= 0. Option C

How to determine the statement

The latest possible time to begin an activity is denoted as LS in project management, while the earliest possible time is indicated by ES.

The distinction between LS and ES signifies the flexibility an activity possesses, allowing it to be postponed without affecting the ultimate timeframe of the project.

The calculation for Slack involves subtracting the earliest possible finish time (LS) from the latest possible finish time (LF). One must note that (LS - ES) will never be negative as the earliest start time (ES) can never be greater than the latest start time (LS).

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Can I get help with number 25 its really hard for me.

Answers

your answer is gonna be -4/3 !!

hi help w/ this question pls i'll give u a brainly

Answers

Answer:

Keep adding 8 56 times subtract three which is 472

Step-by-step explanation:

mulitiply 59 times 8

Derive the following result "algebraically" using the properties listed in Theorem 6.2.2. Give a reason for every step that exactly justifies what was done in the step For all sets A.B.and C.(AU C-B=(A-B)u(C-B)

Answers

we have proven that (A ∪ C) - B = (A - B) ∪ (C - B) algebraically using the properties of set operations

To prove the equality (A ∪ C) - B = (A - B) ∪ (C - B) for all sets A, B, and C, we'll break down the proof step by step, providing a reason for each step based on set operations and properties.

Step 1: Start with the left-hand side (LHS) of the equation: (A ∪ C) - B.

Step 2: Recall that A - B represents the set of elements that are in A but not in B. Similarly, C - B represents the set of elements that are in C but not in B. Therefore, (A ∪ C) - B can be expanded as (A - B) ∪ (C - B).

Step 3: Distribute the union operator (∪) over the set difference (-).

(A ∪ C) - B = (A - B) ∪ (C - B)

Step 4: Apply the distributive property of set operations.

Step 5: We can justify this step by using the definition of set difference and the associative property of the union. For any set X, (X - B) = X ∩ B', where B' represents the complement of set B. Applying this definition to both (A - B) and (C - B), we can rewrite the equation as:

(A ∩ B') ∪ (C ∩ B').

Step 6: Use the distributive property of intersection (∩) over union (∪).

(A ∩ B') ∪ (C ∩ B') = (A ∪ C) ∩ (B' ∪ B')

Step 7: Apply the complement law, which states that B ∪ B' = Universal set (U). Therefore, B ∪ B' = U.

Step 8: Rewrite the equation as (A ∪ C) ∩ U.

Step 9: Applying the intersection of any set X with the universal set U will give the set X itself.

(A ∪ C) ∩ U = A ∪ C.

Therefore, we have proven that (A ∪ C) - B = (A - B) ∪ (C - B) algebraically using the properties of set operations and justifications for each step.

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evaluate the line integral, where c is the given curve. ∫c xy⁴ ds, c is the right half of the circle x² + y² = 9 oriented counterclockwise

Answers

To evaluate the line integral ∫c xy⁴ ds, we need to parameterize the curve c, then substitute into the integrand, and integrate with respect to the parameter.

The right half of the circle x² + y² = 9 can be parameterized as x(t) = 3cos(t), y(t) = 3sin(t) for t in [0, pi]. Note that this parameterization traces out the right half of the circle oriented counterclockwise.

Now, we can express ds as ds = sqrt(dx/dt² + dy/dt²) dt. Using the parameterization x(t) = 3cos(t), y(t) = 3sin(t), we get dx/dt = -3sin(t) and dy/dt = 3cos(t). Thus, ds = sqrt((-3sin(t))² + (3cos(t))²) dt = 3dt.

Substituting x(t) = 3cos(t), y(t) = 3sin(t), and ds = 3dt into the integrand xy⁴, we get xy⁴ = (3cos(t))(3sin(t))⁴ = 81/4 sin⁴(t) cos(t).

So, the line integral becomes:

∫c xy⁴ ds = ∫₀ᴨ (81/4 sin⁴(t) cos(t))(3 dt)

Using trigonometric identities, we can simplify the integrand to:

(81/4)(1/5)(sin⁵(t))' = 81/20 sin⁵(t)

Evaluating the integral from t = 0 to t = pi, we get:

∫c xy⁴ ds = ∫₀ᴨ 81/20 sin⁵(t) dt = 81/16π

Therefore, the value of the line integral is 81/16π.

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Find with proof the sum from i = 1 to n of 2^i for each n >= 1. Find with proof the sum from i = 1 to n of 1/(i(i+1)) for each n >= 1. Prove that n! > 2^n for each n >= 4.


Prove sqrt(2) is irrational.

Find with proof the sum of the first n odd positive integers.



If A is the set of positive multiples of 8 less than 100000 and B is the set of positive multiples of 125 less than 100000, find |A intersect B|.

Find |A union B|.

There are 7 students on math team, 3 students on both math and CS team, and 10 students on math team or CS team. How many students on CS team?

Answers

The sum from i = 1 to n of 2^i is 2(2^n - 1), the sum from i = 1 to n of 1/(i(i+1)) is n/(n+1), n! > 2^n for n ≥ 4, and therefore, sqrt(2) is irrational. The intersection of sets A and B has |A ∩ B| elements, the union of sets A and B has |A ∪ B| elements, and the number of students on the CS team is 6.

Let's break down the questions and provide the proofs and solutions step by step:

Sum of powers of 2: We want to find the sum from i = 1 to n of 2^i for each n ≥ 1. We can use the formula for the sum of a geometric series to simplify the expression:

The sum of a geometric series is given by the formula Sn = a(r^n - 1)/(r - 1), where a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 2, r = 2, and we need to find Sn.

Plugging in the values, we get Sn = 2(2^n - 1)/(2 - 1) = 2(2^n - 1).

Therefore, the sum from i = 1 to n of 2^i is 2(2^n - 1).

Sum of fractions: We want to find the sum from i = 1 to n of 1/(i(i+1)) for each n ≥ 1. We can rewrite the expression as follows:

1/(i(i+1)) = 1/i - 1/(i+1).

Now, we can observe that the terms cancel out in pairs when we sum them. The first term 1/1 remains, and the last term 1/(n+1) remains as well.

Therefore, the sum from i = 1 to n of 1/(i(i+1)) is 1 - 1/(n+1) = n/(n+1).

Proof of n! > 2^n: We will prove this by induction. The base case is n = 4: 4! = 24 > 2^4 = 16.

Now, assume the inequality holds for some k ≥ 4, i.e., k! > 2^k.

We need to prove it for k + 1: (k + 1)! = (k + 1) * k! > (k + 1) * 2^k (since k! > 2^k by the induction hypothesis).

It suffices to show that (k + 1) * 2^k > 2^(k + 1), which simplifies to k + 1 > 2.

Since k ≥ 4, the inequality holds.

Therefore, by induction, we can conclude that n! > 2^n for each n ≥ 4.

Proof that sqrt(2) is irrational: We will prove this by contradiction. Assume that sqrt(2) is rational, i.e., sqrt(2) can be expressed as a ratio of two integers p and q in its simplest form, where q ≠ 0.

sqrt(2) = p/q.

Squaring both sides, we get 2 = p^2/q^2.

Rearranging, we have p^2 = 2q^2.

This implies that p^2 is even, and thus p must be even.

Let p = 2k, where k is an integer.

Substituting back, we have (2k)^2 = 2q^2, which simplifies to 4k^2 = 2q^2.

Dividing by 2, we get 2k^2 = q^2.

This implies that q^2 is even, and thus q must be even.

However, if both p and q are even, then p/q is not in its simplest form, contradicting our initial assumption.

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Help me please I will give points

NO FAKE ANSWERS

Answers

Answer: 2,3,4

Step-by-step explanation:

Apple’s is represented by 8 and oranges is represented by 5. So the ratio 8:5 means every 8 apples their are 5 oranges

consider the following. {(1, −4), (4, 1)} (a) determine whether the set of vectors in rn is orthogonal.

Answers

The given set of vectors which are represented as {(1, -4), (4, 1)} is orthogonal.

To determine whether the set of vectors in ℝⁿ is orthogonal, we need to check if all the pairs of vectors in the set are orthogonal to each other.

In this case, the set of vectors is {(1, -4), (4, 1)}. To determine if these vectors are orthogonal, we calculate their dot product.

The dot product of two vectors (a, b) and (c, d) is given by a * c + b * d.

For the first pair of vectors (1, -4) and (4, 1), the dot product is 1 * 4 + (-4) * 1 = 4 + (-4) = 0.

Since the dot product is zero, we can conclude that the vectors (1, -4) and (4, 1) are orthogonal to each other.

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ou want to put shingles on the outside walls and solar panel the roof of the barn shown. It costs ​$ for each square meter of shingles. Solar panels cost ​$ per square meter. How much will this project​ cost?
4 m
4 m
8 m
9 m
10 m
7 m
5 m

Answers

Something is missing in this question because there are no dollars for the costs... Answer can not be determined.

Hypothesis Testing Prompt Based on a recent study of college students, the average student loan debt amount is $4000. Is the mean student loan debt higher at StatCrunchU? Use Student Loans to conduct the Hypothesis Test and Include each of the following in your response. 1. State your hypothesis in symbolic form and in words. 2. Verify that normality conditions are met. Which test are you using? Why? 3. Use StatCrunch to conduct the hypothesis test. Copy and paste the results (the StatCrunch output window) into your response. 4. Give your P-value and interpret its meaning. 5. Is the mean student loan debt higher at StatCrunchU? State a conclusion that answers the research question. Use a significance level of 5%.

Answers

The actual values (the specific results from StatCrunch, including the p-value) and interpretation would depend on the sample data and the results of the hypothesis test in StatCrunch.

Hypothesis:

Null hypothesis (H0): The mean student loan debt at StatCrunchU is equal to $4000.

Alternative hypothesis (H1): The mean student loan debt at StatCrunchU is higher than $4000.

Normality Conditions and Test Selection:

To verify normality conditions, we need to check if the distribution of student loan debt at StatCrunchU is approximately normal. Since the prompt does not provide any information on the distribution, we will assume that the sample of student loan debt follows a normal distribution. Additionally, we should consider the sample size. If the sample size is large enough (typically considered n ≥ 30), the Central Limit Theorem ensures that the sampling distribution of the mean will be approximately normal, regardless of the underlying distribution of the individual observations.

Hypothesis Test:

To conduct the hypothesis test, we can use a one-sample t-test. We will compare the sample mean of student loan debt at StatCrunchU to the population mean of $4000.

StatCrunch Output:

Unfortunately, as a text-based AI model, I cannot directly access or interact with external tools like StatCrunch to generate real-time output. However, I can guide you through the steps to conduct the hypothesis test using StatCrunch:

Enter the sample data for student loan debt at StatCrunchU.

Select the appropriate options to conduct a one-sample t-test, with a null hypothesis mean of $4000 and an alternative hypothesis mean greater than $4000.

Run the test to obtain the test statistic, degrees of freedom, p-value, and other relevant information.

Copy and paste the results into your response.

P-value and Interpretation:

Once you have conducted the hypothesis test in StatCrunch, you will obtain a p-value. The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.

Using a significance level of 5% (α = 0.05), if the p-value is less than 0.05, we would reject the null hypothesis in favor of the alternative hypothesis. Conversely, if the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis.

Conclusion:

Please provide the specific results from StatCrunch, including the p-value, and I can assist you in interpreting the results and formulating a conclusion based on the research question.

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Diana looks up at an angle of 57 and sees a hot air balloon 150 meters away. To the nearest meter, what is the value of x,
the height of the hot air balloon above Diana's head? (Show work on paper)

Answers

Answer:

230.98 meters

Step-by-step explanation:

Answer:

126m

Step-by-step explanation:

Use sine because we want to find the opposite length but only know the hypotenuse.

Can someone help me with this question. Will Mark brainliest.

Answers

Answer:

Step-by-step explanation:

Write a question that matches this equation:


45-n=15

Answers

Answer:

ayla had 45 cupcakes for the class jayla gave a number out to the cladd Jayla took 15 cupcakes back home what is the does n equal to

You are saving money to buy a car. You put $2500 in a savings account that pays 4% annual interest compounded monthly (hint n = 12). A. Write a function that models the amount of the money in the account over time. B. Find the cost of the car after 10 years.

Answers

Answer:

FV= $3,726.93

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $2,500

Interest rate (i)= 0.04/12= 0.003333 monthly

Number of periods (n)= x months

To calculate the future value giving any number of months, we need to use the following formula:

FV= PV*(1 + i)^n

For 10 years:

n=10*12= 120 months

FV= 2,500*(1.003333^120)

FV= $3,726.93

For the given margin of error and confidence level, determine the sample size required. A researcher wishes to estimate the proportion of fish in a certain lake that are inedible due to pollution of the lake. What sample size will ensure a margin of error of at most 0.053 for a 97.5% confidence interval? In the past, similar research determined that 34% of the fish in the lake are inedible.

Answers

The sample size required to estimate the proportion of inedible fish in the lake with a margin of error of at most 0.053 and a 97.5% confidence level is 491.

To determine the sample size needed for the estimation, we can use the formula:

n = (Z² * p * q) / E²,where:n = sample size,Z = Z-score corresponding to the desired confidence level (in this case, 97.5% corresponds to a Z-score of approximately 1.96),p = estimated proportion of inedible fish (34% or 0.34),q = 1 - p (probability of fish being edible, which is 1 - 0.34 = 0.66),E = margin of error (0.053).

Plugging in these values, we get:

n = (1.96² * 0.34 * 0.66) / 0.053²,n ≈ 491.

Therefore, a sample size of 491 will ensure a margin of error of at most 0.053 for a 97.5% confidence interval when estimating the proportion of inedible fish in the lake.

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what is the factorization of the polynomial below 16x2-9

Answers

Answer:

(4x - 3)(4x + 3)

Step-by-step explanation:

16x² - 9 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

16x² - 9

= (4x)² - 3²

= (4x - 3)(4x + 3)




1. The three year discount factor is 0.7773 and the one year discount factor is 0.9434. Calculate the two year discount factor if the three year annuity factor is 2.6065 a. 0.9623 b. 0.8758 c. 0.9132

Answers

After considering the given data we conclude that the generated two year discount factor is 0.9132, under the condition that three year annuity factor is 2.6065.

Applying the formula for the annuity factor, we can find the two year discount factor:
[tex]annuity factor = (1 - discount factor^n) / r[/tex]
Here,
n = number of years
r = annual interest rate.
We are given that the three year discount factor is 0.7773 and the one year discount factor is 0.9434. We are also given that the three year annuity factor is 2.6065.
Applying the formula for the annuity factor, we can evaluate the annual interest rate:
[tex]2.6065 = (1 - 0.7773^3) / r[/tex]
r = 0.1
Now, we can evaluate the two year discount factor:
[tex]annuity factor = (1 - discount factor^2) / 0.1[/tex]
[tex]2.6065 = (1 - discount factor^2) / 0.1[/tex]
[tex]discount factor^2 = 0.89335[/tex]
discount factor = [tex]\sqrt(0.89335)[/tex]
discount factor = 0.9132
Therefore, the two year discount factor is 0.9132.
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The sum of two numbers is 48. The second number is twice the first
Write and solve a system of equations to find the numbers.

Answers

Answer:

The equations are

X + Y = 48 ----Eq (1)

Y = 2 X -----Eq (2)

Solution of the equations and the two number are

X = 16, Y = 32

Step-by-step explanation:

Let the two numbers be X and Y

Given -

The sum of two numbers is 48.

Thus, X + Y = 48 ----Eq (1)

The second number is twice the first

Thus, Y = 2 X -----Eq (2)

Substituting the value of Y in equation (1), we get -

X + 2X = 48

3 X = 48

X = 16

Y = 2 X = 32

Which is a better price: 5 for $1,4
for $0.85, 2 for $0.38, or 6 for
$1.10?

Answers

Answer:

6 for $1.1

Step-by-step explanation:

6 for $1.1 is the answer

Equation of the line pls help

Answers

-2x+5 is the equation of the line

Use Rouché's Theorem to find the number of (complex) roots, counting multiplicities, of 2z8 + 3z5 - 9z³ + 2 = 0 in the region 1 < |z| < 2.

Answers

To apply Rouché's Theorem, we consider two functions: f(z) = 2z⁸ + 3z⁵ - 9z³ + 2 and g(z) = 2z⁸. We want to analyze the number of roots of f(z) = 0 inside the region 1 < |z| < 2.

First, let's examine the behavior of f(z) and g(z) on the boundary of the region. When |z| = 1, the term 2z⁸ dominates over the other terms in f(z), so |f(z)| < |g(z)|. On the other hand, when |z| = 2, the term 2z⁸ is still dominant, and again |f(z)| < |g(z)|.

Since |f(z)| < |g(z)| on the boundary of the region, Rouché's Theorem guarantees that f(z) and g(z) have the same number of roots inside the region, counting multiplicities. In this case, g(z) = 2z⁸ has exactly eight roots, counting multiplicities.

Therefore, by Rouché's Theorem, we can conclude that the equation 2z⁸ + 3z⁵ - 9z³ + 2 = 0 has eight roots, counting multiplicities, inside the region 1 < |z| < 2.

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On a 50-point quiz, Jenna earned 82%
of the points. How many points did she
earn?

Answers

Answer:

x=41

Step-by-step explanation:

x/50=82/100

cross multiply

100x= 82×50

100x= 4100

x= 4100/100

x= 41

check our work

41/50 × 100= 82 percent

41
have a great day :)

A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. What is the direction of the magnetic field at a point P due to this wire? Q Tap image to zoom 0 along the +x-axis 0 out of the plane of the page 0 along the -x-axis 0 into the plne of the page into the plane of the page 0 along the ty-axis

Answers

The  direction of the magnetic field at P is perpendicular to both the current direction and the direction of the curl of our fingers.

The direction of the magnetic field at point P due to the current-carrying wire can be determined using the right-hand rule. If we point our right thumb in the direction of the current (which is along the positive x-axis), and curl our fingers toward the point P, then the direction of the magnetic field at P is perpendicular to both the current direction and the direction of the curl of our fingers.

In this case, since the wire is straight and lies in the x-y plane, the direction of the magnetic field at point P will be perpendicular to the plane of the page, and will either be pointing into or out of the page. To determine which direction, we need to know the orientation of point P relative to the wire. If point P is above the wire, then the magnetic field will be pointing into the page, and if it is below the wire, then the magnetic field will be pointing out of the page.

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In the accompanying diagram of triangle ABC , D is a point on AC , AB is extended to E, and DE is drawn so that triangle ADE~ triangle ABC . If m

Answers

Answer:

m∡ADE = 80°

Step-by-step explanation:

m∡ADE = m∡ABC

m∡B = 180-(30+70) = 80°

therefore, m∡ABC = 80° and so does m∡ADE because they are congruent

Gina had 1/2 a liter of Dr. Pepper. She gave 2/5 of a liter to her friend. How much does she have left?

Answers

Answer:

1/10

Step-by-step explanation:

1) find a common factor between the two denominators.

2 and 5 have a common factor of 10. you can find this by multiplying the denominators.

2) now that you have a common denominator of 10, you'll need to change the numerators too. you do this by finding out how many times the denominator goes into your common factor. 5 goes into 10 two times so you would multiply 2 x 2. two goes into 10 five times so multiply 5 x 1.

3) you now have both fractions that share a common factor. now you have to subtract them.

5/10 - 4/10 = 1/10

I need help on this question

Answers

The correct answer is c.3/2


what value would make the set of points a function. (9, -2) (4,
3) (8,10) (? , 8)

Answers

Answer:

Any x-value other than 4, 8, or 9 would make this set of points a function.

Other Questions
How do I write [tex]\sqrt[4]{5}[/tex] using rational exponets? Let : R R2 given by (r,0) = (r cos(0), r sin(0)), 0 r R, 00 2m (this is a disk of radius R centered at (0,0)). Compute fdx . Can someone plz help, I got some of it but not all Which statement best explains the role of Jefferson Davis during the Civil War?Select one:a) A former U.S. Cabinet member, he was elected as President of the Confederacy.b) He surrendered Confederate troops to Union forces at Appomattox Court House in 1865.c) He was offered command of Union troops by President Lincoln but joined the Confederacy instead when his own state of Virginia seceded.d) He commanded Confederate troops at the Battle of Gettysburg, which proved to be a turning point in the war. Most people live in this part of the Western Region due to it's closeness to the ocean and abundant plant life (Sub Saharan Africa)A) SouthB) NorthC) EastD) West Exercise 1.5.9 Let R be an n x n upper-triangular matrix with semiband width s. Show that the system Rx = y can be solved by back substitution in about 2ns flops. An analogous result holds for lower-triangular systems. In a set of 1,000 integers from 1 to 1,000, an integer chosen at random on a single trial should be an integer from 1 to 25 about 25 out of every 1,000 trials, or one out of every 40 integers selected. A sample of 5 integers selected is shown. Does this sample represent the general rule for picking an integer from 1 to 25 in the population of integers from 1 to 1,000? A. Yes - the sample is representative of the expected number of integers from 1 to 25 in a sample of 5 integers, which would be none or zero.B. No - the sample is not representative of the expected number of integers from 1 to 25 in a sample of 5 integers, which would be at least 10.Reminder: Make sure to include your work!!! Read the following excerpt from a narrative about a hike in the woods:(1) The cicadas buzzed in the distance, and Meredith wiped the sweat from her forehead. (2) She was dressed head-to-toe in khaki, her cargo shorts stuffed with every possible tool she could need. (3) She had a compass, a map, a water bottle, and a travel-sized container of bug repellant. (4) The woods practically pulsed with life around her.Which sentence contains descriptive details that bring the main character to life? A. sentence 1; It shows that Meredith is sweating. B. sentence 2; It helps us picture what she looks like. C. sentence 3; It describes the contents of her pockets. D. sentence 4; It helps us picture where Meredith is. What do studies of adopted children, identical twins, and fraternal twins reveal about the relationship between obesity and genetics?Question 9 options:There does not appear to be any relationship between heredity and body type or level of fatness.Body type seems to be a function of heredity, while level of fatness appears to be influenced primarily by environment.Fatness levels appear to be influenced by heredity, while body type seems to be a function of environment.Both body type and level of fatness seem to be influenced by heredity. Can someone please help!!!Ill give brainliest!! The compression of matter due to gravitational attraction increased as the protoplanets formed. What was a result of this compression within each protoplanet?A. initiation of nuclear fusionB. increase in noble gas destabilizationC. increase in thermal energyD. initiation of photosynthesis reactions Which of the following is arepresentation of 11! Does the Christensen article support Porter's concept of strategy? Does Dawar?Porter, "What is Strategy?" Harvard Business Review, November 1996, 61-78.Christensen, Anthony, Berstell and Nitterhouse, "Finding the Right Job For Your Product", MIT Sloan Management Review, Spring 2007, 38-47.Dawar, "When Marketing Is Strategy", Harvard Business Review, December 2013, 101-108 Write a program that will ask the user for a set of ten numbers. After all ten numbers have been entered, the program will display the largest and smallest numbers of the data set. The program will then prompt the user whether he/she would like to enter another set of data. When the user indicates he/she is finished entering data sets, the program will finally display the average largest number and the average smallest number for all sets entered. Regional economic integration offers the following benefits EXCEPT:a. Access to a larger market.b. Common languagec. Simpler product standardsd. Reduced distribution costs select the two comorbid disorders with which pica occurs most commonly. Zeynep's coffee and movie budget is $20 a week. The price of a cup of coffee is $5 and the price of a movie ticket is $2. Which of the following statements is true? a. When Zeynep spends all her income on movies, she can see 10 movies per week. b. When Zeynep buys 4 cups of coffee per week, she has no money left to buy a movie ticket. c. Zeynep can afford to buy two cups of coffee and five movie tickets per week. d. Zeynep can afford to buy three cups of coffee and six movie tickets per week. e. Options A, B, and C are all correct. Jared gets 10 heads when flipping a weighted coin 12 times. Based on experimental probability, how many of the next six flip should Jared expect to come up heads? Select all possible cross sections of a sphere.circleBsquareCtriangleDpoint Arrange the following 0.10 M solutions from most acidic to most basic. Justify your rankings.KOHKNO3KCNNH4ClHCl