All integer solutions to the given equation 24x + 9y = 33 is (1,1).
To find all integer solutions to the equation 24x + 9y = 33, we can use a method called "Diophantine equations".
First, we need to find the greatest common divisor (GCD) of 24 and 9. The GCD of 24 and 9 is 3.
Next, we divide both sides of the equation by the GCD, which gives us:
8x + 3y = 11
Now, we can use a method called "Euclidean algorithm" to find the solutions for x and y.
Step 1: Let y = 0, then we have 8x = 11, which has no integer solutions.
Step 2: Let y = 1, then we have 8x + 3 = 11, which gives us x = 1. Therefore, one solution is (1,1).
Step 3: Let y = 2, then we have 8x + 6 = 11, which gives us x = 1/2, which is not an integer.
Step 4: Let y = 3, then we have 8x + 9 = 11, which gives us x = 1/4, which is not an integer.
Therefore, the only integer solution to the equation 24x + 9y = 33 is (1,1).
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Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x = 96.62, y= 94.75, r=0.879, P-value = 0.000, and ŷ = -2.59 + 1.01x, where x represents the IQ score of the twin born first. Find the best predicted value of ý given that the twin born first has an IQ of 109?
Answer:the best predicted value of ý when the twin born first has an IQ of 109 is 107.50
Step-by-step explanation:
Given the regression equation:
ŷ = -2.59 + 1.01x
We need to predict the value of ý when x (IQ score of the twin born first) is 109.
So we substitute x = 109 into the regression equation:
ŷ = -2.59 + 1.01(109)
ŷ = -2.59 + 110.09
ŷ = 107.50
Therefore, the best predicted value of ý when the twin born first has an IQ of 109 is 107.50.
please help will mark brainliest
Answer:
5/6
Step-by-step explanation:
create a proportion:
(1/2÷3/5) = (x÷5/5)
cross-multiply to solve for 'x':
3/5x = 1/2
6x = 5
x = 5/6
Answer:
\(\frac{5}{6}\)
Step-by-step explanation:
Ok so one hour is 1/1.
1/1 - 3/5 = 2/5
So Landon has 2/5 of an hour left.
Let's find out how much 1/5 of an hour is in the test.
1/2 ÷ 3 = 1/6
So 1/5 of an hour = 1/6 of the test.
1/6 * 2 = 1/3
1/2 + 1/3 = 5/6
POSSIBLE POINTS: 1.43
Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not
come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's?
Answer:
it will take 25 months until the cost is the same.
500 / 20 = 25
Step-by-step explanation:
One minus the quotient of one and a number x
Answer:
1/x-1
Step-by-step explanation:
im confused how many solutions are parellel lines and how many solutions are intersecting lines
Answer:
There are no solutions to paralell lines and there is exactly one solution to intersecting(perpendicular) lines.
Step-by-step explanation:The solutions would be the point of intersection and paralell lines never meet at any points. Interesecting lines intersect at exactly one point, which proves my answer above. Hope this helped
what is x - (14x-4) + 12 = 6x + 32
Answer:
x= -16/19
Step-by-step explanation:
x−14x+4+12=6x+32
−13x+16=6x+32
16=6x+32+13x
16=19x+32
16−32=19x
−16=19x
-16/19=x
Please answer quick asap
Answer:
1,024
Step-by-step explanation:
someone help i'll give brainliest to right answer!
QUESTION: A pentagon has angles that measure 110°, 90°, 80°, 115°, and v. What is v?
Answer:
145
Step-by-step explanation:
angles in a pentagon add up to equal 540
Hence, 110 + 90 + 80 + 115 + v = 540
( note that we just created an equation that we can use to solve for v )
We now solve for v using the equation created
110 + 90 + 80 + 115 + v = 540
step 1 combine like terms
110 + 90 + 80 + 115 = 395
we now have 395 + v = 540
step 2 subtract 395 from each side
540 - 395 = 145
395 - 395 cancels out
we're left with v = 145
what is the independent variable in this example HURRY PLEASE
Answer:
Volume
Step-by-step explanation:
x axis is always independant y axis is always dependant
the graph of F(x) shown below resembles the graph of G(x) =x^2 but it has been changes somewhat. Which of the following could be the equation of F(x)
Using translation concepts, the equation of the graph F(x) is given as follows:
F(x) = -x² - 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, the graph of G(x) = x² was reflected over the axis(multiplied by -1), and shifted down 3 units(F(x) -> G(-x) - 3), hence the equation for F(x) is:
F(x) = -x² - 3.
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EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-
(if you put links or don't answer accordingly im reporting your account)
Answer:
see below
Step-by-step explanation:
Proposition:Let the diagonals AC and BD of the Parallelogram ABCD intercept at E. It is required to prove AE=CE and DE=BE
Proof:1)The lines AD and BC are parallel and AC their transversal therefore,
\( \displaystyle \angle DAC = \angle ACB \\ \ \qquad [\text{ alternate angles theorem}]\)
2)The lines AB and DC are parallel and BD their transversal therefore,
\( \displaystyle \angle BD C= \angle ABD \\ \ \qquad [\text{ alternate angles theorem}]\)
3)now in triangle ∆AEB and ∆CED
\( \displaystyle \angle EAD=\angle ECB\)\(\angle EDA=\angle EBC\)\( \displaystyle AD=BC\)therefore,
\( \displaystyle \Delta AEB \cong \Delta CED \)
hence,
AE=CEDE=BEProven
please help with easy math triangle question
Answer:
not sure but i think its 12
Step-by-step explanation:
if you look carefully one side witch is 6 is have of side x and 6 x 2 is 12
hope this helps.
Answer:I think its 15 but I'm not sure
Step-by-step explanation:
5t + 15 ≥ 50
What's the answer?
Answer:
Subtract 15 from both sides.
5t > 35
Divide both sides by 5.
t > 7
(Sorry, I can't do the > with the _ under it.)
Please mark me Brainliest; I need it to move onto the next level. =D
I need help with this
By applying Pythagoras' theorem, the length of x is equal to 10 units.
How to calculate the length of x?In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:
x² = y² + z²
x² = 8² + 6²
x² = 64 + 36
x = √100
x = 10 units.
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find the square root of 484 by using prime factorization. { show step by step working and tree ]
By prime factorization and properties for radical functions, we conclude that the square root of 484 is equal to 22.
What is the square root of a natural number by using prime factorization?
There are two kinds of natural numbers: prime numbers and compound numbers. Prime numbers are numbers that are only divided by 1 and by itself and compound numbers are numbers that are products of prime numbers.
First, we determine the form of 484 as a product of prime numbers:
484 = 242 × 2
484 = 121 × 2²
484 = 2² × 121
484 = 2² × 11²
Finally, we proceed to obtain the square root of 484 by applying square roots on both sides of the equation and properties for radical functions:
√484 = √(11² × 2²)
√484 = √11² × √2²
√484 = 11 × 2
√484 = 22
By prime factorization and properties for radical functions, we conclude that the square root of 484 is equal to 22.
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The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 600 1000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is a. 150. b. 200. c. .25. d. .33.
The expected number of adults who prefer coffee is 150.
We must determine the anticipated number of adults who prefer coffee in order to test for independence between age and drink preferences.
First, let's look at the totals of the rows and columns to figure out the expected values for each category. The formula is available to us:
Anticipated esteem = (Line absolute * Section complete)/Stupendous aggregate
The stupendous complete for this situation is 1000.
Number of adults expected to prefer coffee:
= (Adults total minus Coffee total) / Grand total = (600 minus 250) / 1000 = 150; consequently, 150 adults are anticipated to prefer coffee.
In this way, the right response is (a) 150.
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Which of the following expressions is equivalent to 810 x 9?
O (800 x 9) + (10 x 9)
O (81 x 9) + (10 x 9)
O (600+ 310) x 9
O
814 x 5
Answer:
(800 x 9) + (10 x 9)
Step-by-step explanation:
Find out what 810 x 9 is:
810 x 9 = 7290
Then see which expression has the same answer. Personally I'd check all of them, but luckily the first expression is the correct one so you don't need to go through the rest (since it only asks for one correct expression):
(800 x 9) = 7200
(10 x 9) = 90
7200 + 90 = 7290
The area of quadrilateral ABCD in the below figure is
(a) 57 cm
(b) 95 cm2
(c) 102 cm2
(d) 114 cm
Answer:
a)57
Step-by-step explanation:
PLEASE HELP!!! Find the slope of each side of the triangle.
9514 1404 393
Answer:
AB: -3BC: 2/3AC: -1/4Step-by-step explanation:
The slope of a given segment is the ratio rise/run. The "rise" is the number of vertical divisions between the points. The "run" is the number of horizontal divisions between the points. The "run" is positive left-to-right. The corresponding "rise" is positive up.
Here are the segment slopes (rise/run).
AB = -3/1 = -3
BC = 2/3
AC = -1/4
the adult men of the dinaric alps have the highest average height of all regions. the distribution of height is approximately normal with a mean height of 6 ft 1 in (73 inches) and standard deviation of 3 inches. what percentage of men have a height between 68 and 72 inches?
Approximately 34.13% of men in the Dinaric Alps region have a height between 68 and 72 inches.
To calculate this percentage, we need to find the area under the normal distribution curve between 68 and 72 inches. We can do this by standardizing the values using the z-score formula:
z = (x - μ) / σ
where x is the height value, μ is the mean height, and σ is the standard deviation.
For x = 68 inches, the z-score is:
z = (68 - 73) / 3 = -1.67
For x = 72 inches, the z-score is:
z = (72 - 73) / 3 = -0.33
Using a standard normal distribution table or a calculator with a normal distribution function, we can find that the area under the curve between z = -1.67 and z = -0.33 is approximately 0.3413 or 34.13%. Therefore, approximately 34.13% of men in the Dinaric Alps region have a height between 68 and 72 inches.
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what is the angle taken in clockwise direction between : (1) North- east and north- west .
Answer:
I think the answer is both
Answer
hope this helps
∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.5 to form ∆PQR . The side lengths of ∆ABC are AB =5 units; BC = 4.2 units; and AC = 4 units. Find the length of PQ, QR and PR.
A. PQ = 6, QR = 6.3 and PR = 7.5.
B. PQ = 7.5, QR = 6 and PR = 6.3.
C. PQ = 6.3, QR = 7.5 and PR = 6
D. PQ = 7.5, QR = 6.3 and PR = 6.
PLEASE HELP QUICK! this is due in 10 minutes:(
Answer:
Given that the triangle ABC is dilated by a scale factor of 1.25 to form the new triangle PQR, the dimensions of PQR will be as follows;
AB corresponds to PQ, but the length of AB=5 units, the length of PQ will be:
PQ=5*1.25=6.25 units
BC corresponds to QR, but the length if QR=4.2 units, the length of QR will be:
QR=4.2*1.25=5.25 units
lastly,
CA corresponds to RP, but CA=4 units, therefore RP will be:
4*1.25=5 units
8) Find x. (Type just the number as your answer.)
64°
X
45°
Answer:
I believe the answer is 71 degrees. Don't quote me on it though. lol
Step-by-step explanation:
Fill in the gaps to factorise this expression.
x²
x +5x – 14 = (x− _)(x + _)
Answer:
the answer is
x +5x – 14 = (x− 2 )(x + 7)
The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?.
Since the ages of students at a university are normally distributed with a mean of 21, the percentage of the student body that is at least 21 years old is: 50%.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean have a higher frequency than the data that are far from the mean.
For all normal distributions, the mean is always located at the center with 50 percent (50%) or 0.5 of the distribution to either side, which is right or left of the distribution.
In this context, the percentage of student body that is at least 21 years old is represented by the percentage to the left of the normal distribution, which is 50 percent (50%):
P(x ≤ 21) = 50%
P(x ≤ 21) = 50/100
P(x ≤ 21) = 0.5.
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Multiply as indicated. Write the product in standard form.
(2+i)^2
Answer:
3 + 4i
Step-by-step explanation:
Let \( f(x)=-x^{2}-5 x-6 \) and consider the statements given below. Select all statements that are true of f(x) is always increasing. f(x) is always decreasing. f(x) has a local minimum. f(x) has a local maximum. f(x) is concave down. f(x) is concave up. f(x) has an inflection point.
"
The statements that are true for the function f(x) = -x² - 5x - 6 are:
1. f(x) has a local maximum.
2. f(x) is concave down.
3. f(x) has an inflection point.
1. f(x) has a local maximum:
Taking the derivative of f(x) gives f'(x) = -2x - 5. The derivative is a linear function with a negative slope (-2), indicating that f(x) is decreasing. Therefore, f(x) has a local maximum.
2. f(x) is concave down:
To determine the concavity of f(x), we need to analyze the second derivative, f''(x). Taking the second derivative of f(x), we get f''(x) = -2. Since the second derivative is a constant (-2) and negative, f(x) is concave down.
3. f(x) has an inflection point:
An inflection point occurs when the concavity of a function changes. Hence, f(x) does not have an inflection point.
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Complete question - Let f(x) = -x² - 5x - 6 and consider the statements given below. Select all statements that are true.
f(x) is always increasing.
f(x) is always decreasing.
f(x) has a local minimum.
f(x) has a local maximum.
f(x) is concave down.
f(x) is concave up.
f(x) has an inflection point.
Information technology supports supply chain integration through information sharing and collaborative planning. workflow coordination. adoption of new methods and technologies. all of these answer choices are correct.
By leveraging information technology effectively, supply chain integration can be achieved, leading to improved collaboration, streamlined processes, reduced costs, and enhanced overall supply chain performance.
What is chain integration?A comprehensive corporate approach known as supply chain integration aims to improve communication and cooperation between all chain nodes.
All of the answer choices provided are correct. Information technology plays a crucial role in supporting supply chain integration by facilitating information sharing, collaborative planning, workflow coordination, and the adoption of new methods and technologies.
1. Information sharing: Information technology enables the exchange of data and information among different entities within the supply chain, such as suppliers, manufacturers, distributors, and retailers. This sharing of information helps improve visibility, transparency, and coordination among the various stakeholders.
2. Collaborative planning: Information technology tools and systems enable collaborative planning processes, where different participants in the supply chain can collaborate on forecasting, demand planning, inventory management, and production scheduling. This collaboration enhances efficiency, reduces costs, and improves overall supply chain performance.
3. Workflow coordination: Information technology facilitates the coordination of workflows and processes across different stages of the supply chain. It enables real-time tracking and monitoring of goods, enables efficient communication and coordination between different parties involved, and helps streamline and automate various supply chain activities.
4. Adoption of new methods and technologies: Information technology enables the adoption and implementation of new methods, strategies, and technologies within the supply chain. This includes the use of advanced analytics, cloud computing, Internet of Things (IoT), artificial intelligence (AI), and other digital solutions that enhance efficiency, visibility, and decision-making capabilities within the supply chain.
By leveraging information technology effectively, supply chain integration can be achieved, leading to improved collaboration, streamlined processes, reduced costs, and enhanced overall supply chain performance.
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A test for ovarian cancer has a 5 percent rate of false positives and a 0 percent rate of false negatives. On average, 1 in every 2,500 American women over age 35 actually has ovarian cancer. If a woman over 35 tests positive, what is the probability that she actually has cancer? Hint: Make a contingency table for a hypothetical sample of 100,000 women. Explain your reasoning.
Given the provided information, if a woman over 35 tests positive for ovarian cancer, the probability that she actually has cancer is approximately 1.96%.
To determine the probability that a woman over 35 actually has ovarian cancer given a positive test result, we can create a contingency table and use conditional probability. Let's consider a hypothetical sample of 100,000 women:
Out of 100,000 women, 1 in every 2,500 (or 40 out of 100,000) actually has ovarian cancer. Since the test has a 0% rate of false negatives, all the women with ovarian cancer will test positive.
The test also has a 5% rate of false positives. This means that out of the remaining 99,960 women who do not have ovarian cancer, approximately 5% (or 4,998) will test positive incorrectly.
Therefore, out of a total of 5,038 positive test results (40 true positives + 4,998 false positives), only 40 are true positives for ovarian cancer. The probability that a woman who tests positive actually has ovarian cancer can be calculated as the ratio of true positives to the total positive tests:
Probability = (True Positives) / (Total Positive Tests) = 40 / 5,038 ≈ 0.00795 ≈ 0.795%
Thus, the probability that a woman over 35 actually has ovarian cancer given a positive test result is approximately 1.96%. This calculation highlights the importance of considering both the prevalence of the disease and the accuracy of the test in interpreting the results correctly.
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Suppose federal government spending for a popular housing program was $1 billion this year and congress has proposed increasing spending for the program to $1.01 billion for next year. assume that the consumer price index is expected to rise by 3% over the next year. those who support the program complain that the program is being cut. those who oppose the program complain that the program is being increased. explain each position.
The supporters of the program complain that it is being cut because the increase in spending is not enough to keep up with inflation.
The opponents of the program complain that it is being increased because any additional funding is seen as unnecessary or undeserved.
The supporters of the housing program complain that the program is being cut because they believe that the increase in spending is not enough to keep up with the expected 3% rise in the consumer price index.
They argue that if the spending does not increase at the same rate as the inflation, the program will actually have less purchasing power and be less effective in addressing housing needs.
On the other hand, the opponents of the housing program complain that the program is being increased. They argue that any increase in spending, even if it is not keeping up with the expected rise in the consumer price index, is still an increase compared to the current budget.
They believe that the program should not receive any additional funding or even that the funding should be reduced.
So, to summarize, the supporters of the program complain that it is being cut because the increase in spending is not enough to keep up with inflation.
The opponents of the program complain that it is being increased because any additional funding is seen as unnecessary or undeserved.
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