Let x be the number of GMC sold
Let y be the number of Honda soldAccording to the given data, we can form the following equations: x+y = 175 ............ (1)300x + 450y = 60,750 ............ (2)
Multiplying equation (1) by 300 on both sides, we get:300x + 300y = 52,500Subtracting this equation from equation (2), we get:150y = 8,250Solving for y, we get:y = 55Substituting the value of y in equation (1),
we get:x + 55 = 175x = 120Therefore, the number of GMCs sold is 120 and the number of Hondas sold is 55.
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The company have sold 50 GMC and 125 Honda for this profit.
Let the number of GMC sold be x and the number of Honda sold be y.
Then:
[tex]x + y = 175[/tex]----------------------(1)
GMC: Profit on one car sold = $300
Therefore, the total profit on x GMC cars sold = $300x
Honda: Profit on one car sold = $450
Therefore, the total profit on y Honda cars sold = $450y
Total profit on x GMC and y Honda sold = $60,750
Therefore, we can write:
[tex]300x + 450y = 60,750[/tex]----------------(2)
Multiplying (1) by 450 and subtracting it from (2) multiplied by 100, we get:
[tex]-150x = 7,500⇒ x = 50[/tex]
Substituting the value of x in (1), we get:
[tex]y = 175 - 50= 125[/tex]
Therefore, the number of GMC sold is 50 and the number of Honda sold is 125.
They have sold 50 GMC and 125 Honda.
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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.
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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I need help on this question
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?
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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consider the following. {(1, −4), (4, 1)} (a) determine whether the set of vectors in rn is orthogonal.
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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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
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
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.
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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Write a question that matches this equation:
45-n=15
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
Can someone help me with this question. Will Mark brainliest.
Answer:
Step-by-step explanation:
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?
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
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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how do you determine a function if a relation is a function
Answer:
Hello! A function is easily identified when an x value does not have more than 1 y value. a y value can have as many x values to infinity, but x can only have one y.
Example...
x y
3 5
4 5
1 2
Can I get help with number 25 its really hard for me.
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%.
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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hi help w/ this question pls i'll give u a brainly
Answer:
Keep adding 8 56 times subtract three which is 472
Step-by-step explanation:
mulitiply 59 times 8
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
Is the following equation true? 4m + 12 = 2(m + 6)
Answer:
no
Step-by-step explanation:
4m + 12 ≠ 2m + 12
PLZZ ILL GIVE BRAINLIESTTT
Answer:
give me poi tasjnsaklaalwkdbfbdjwo
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.
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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Which of the following is true?
Group of answer choices
(LF – LS) > (EF – ES)
Slack = (LF – LS)
(LS – ES) >= 0
The statement that is true is (LS – ES) >= 0. Option C
How to determine the statementThe 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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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)
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
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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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)
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.
what value would make the set of points a function. (9, -2) (4,
3) (8,10) (? , 8)
Answer:
Any x-value other than 4, 8, or 9 would make this set of points a function.
Which is a better price: 5 for $1,4
for $0.85, 2 for $0.38, or 6 for
$1.10?
Answer:
6 for $1.1
Step-by-step explanation:
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.
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
Equation of the line pls help
On a 50-point quiz, Jenna earned 82%
of the points. How many points did she
earn?
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
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?
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
assume x and y are functions of t. evaluate for 2xe^y, with the conditions , x, y0.
The expression to evaluate is 2xe^y, where x and y are functions of t, and the initial conditions are given by x(t=0) = x_0 and y(t=0) = y_0.
To evaluate 2xe^y, we substitute the values of x and y in terms of t into the expression. Since x and y are functions of t, we need to know their specific forms or have additional information about them to proceed with the evaluation.
Without knowing the explicit expressions for x and y or any additional information, we cannot provide a specific numerical evaluation of 2xe^y. However, if you have the specific forms of x(t) and y(t) or any other relevant information, please provide them so that we can assist you further in evaluating the expression.
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what is the factorization of the polynomial below 16x2-9
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)