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for the following question(s): a school counselor tests the level of depression in fourth graders in a particular class of 20 students. the counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. on the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. from reports, she is able to find out about past testing. fourth graders at her school usually score 5 on the scale, but the variation is not known. her sample of 20 fifth graders has a mean depression score of 4.4. suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. she figures her t score to be 2.8. what decision should she make regarding the null hypothesis? group of answer choices postpone any decisions until a more conclusive study could be conducted fail to reject it there is not enough information given to make a decision reject it
Answers
Answer:
Based on the information provided, the correct choice is:
fail to reject it
Here are the key points:
• The mean depression score for the sample of 20 4th graders was 4.4.
• The counselor tested the null hypothesis that these 4th graders were less depressed than the general 4th grader population.
• The t score calculated was 2.8.
To reject the null hypothesis and conclude the sample differs from the population, we would need a high enough t score. But the t score of 2.8 is not conclusively high enough here.
Some additional considerations:
• The general 4th grader population mean is 5, so the sample mean of 4.4 is a bit lower, but not drastically. This suggests the sample may not differ hugely from the population.
• There is no information on the variation or standard deviation for either the sample or population. Without this, we can't determine if a t score of 2.8 actually signifies a statistically significant difference.
• The sample size of 20 is decent but not very large. Larger sample sizes provide more conclusive results.
• No p-value is given, making it hard to judge if the t score of 2.8 is high enough to reject the null hypothesis. By convention, p<0.05 is often used but we don't have the p-value here.
So overall, there is not enough definitive evidence provided to conclusively reject the null hypothesis. The t score of 2.8 alone is probably not high enough, given the considerations around sample size, variation, and lack of a p-value. More data and analysis would be needed to make a firm decision either way.
Therefore, the correct choice is: "fail to reject it". There is not enough information given in this question and results to conclusively reject the null hypothesis.
Step-by-step explanation:
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2). Match the coordinates of the points of the transformed polygons to their correct values. the coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ (-2, 2) the coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ (4, -2) the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ (3, -1) the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ (4, 2) arrowBoth arrowBoth arrowBoth arrowBoth
Answers
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).
If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x).
If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).
If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).
The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)
The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).
the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)
the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)
Answer:
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).
If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x).
If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).
If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).
Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).
The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)
The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).
the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)
the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)
Step-by-step explanation:
if a bag contains 18 different-colored marbles, how many different samples of 3 marbles can be drawn from the bad?
Answers
There are 136 different samples of 3 marbles that can be drawn from the bag containing 18 different-colored marbles.
To determine the number of different samples of 3 marbles that can be drawn from a bag containing 18 different-colored marbles, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n - r)!)
Where:
n is the total number of items to choose from (18 marbles in this case).
r is the number of items to choose (3 marbles in this case).
"!" denotes the factorial operation, which means multiplying a number by all the positive integers less than it.
Let's calculate the number of different samples of 3 marbles:
C(18, 3) = 18! / (3!(18 - 3)!)
Calculating the factorials:
18! = 18 × 17 × 16 × ... × 1
3! = 3 × 2 × 1
(18 - 3)! = 15! = 15 × 14 × 13 × ... × 1
Simplifying the expression:
C(18, 3) = (18 × 17 × 16 × ... × 1) / ((3 × 2 × 1) × (15 × 14 × 13 × ... × 1))
Cancelling out common terms:
C(18, 3) = (18 × 17 × 16) / (3 × 2 × 1)
C(18, 3) = (816) / (6)
C(18, 3) = 136
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16PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
Answers
Answer: C
Step-by-step explanation:
For our unknown value x, the opposite side = 10 and the adjacent side = 18, using this information you can use SOH CAH TOA.
TOA refers to opposite over adjacent, which would be
tan x = 10/18.
Hope this helps!
An object is launched vertically in the air at 41.65 meters per second from a 7-meter-tall platform. using the projectile motion model h(t)=-4.9t^2+v0t+h0, where h(t) is the height of the projectile t seconds after it’s departure, v0 is the initial velocity in meters per second, and h0 is the initial height in meters, determine how long it will take for the object to reach its maximum height. what is the maximum height?
Answers
To find the maximum height of the object, we need to first determine when the object reaches that height. We can use the projectile motion model h(t) = -4.9t^2 + v0t + h0 to solve for the time it takes for the object to reach its maximum height.
Since the object is launched vertically, we know that its initial velocity is 41.65 m/s and its initial height is 7 meters. We can substitute these values into the projectile motion model and solve for when the object reaches its maximum height by finding the vertex of the resulting quadratic function.
h(t) = -4.9t^2 + 41.65t + 7
To find the time it takes for the object to reach its maximum height, we can use the formula t = -b/2a, where a = -4.9 and b = 41.65.
t = -(41.65)/(2(-4.9))
t = 4.25 seconds
Therefore, it takes 4.25 seconds for the object to reach its maximum height.
To find the maximum height, we can plug in this time value into the projectile motion model and solve for h(t).
h(4.25) = -4.9(4.25)^2 + 41.65(4.25) + 7
h(4.25) = 89.57 meters
The maximum height of the object is 89.57 meters.
In summary, the object launched vertically from a 7-meter-tall platform with an initial velocity of 41.65 m/s takes 4.25 seconds to reach its maximum height of 89.57 meters. This is found by using the projectile motion model h(t) = -4.9t^2 + v0t + h0 and finding the time it takes for the object to reach its maximum height, and then plugging in that time value to find the maximum height.
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Answer these two and I'll make as brainest.
Answers
Answer:
25x + 5 equals 130, x=5, (2) x= 6 10x=60 degrees
Step-by-step explanation:
justify each statement below using a property of equality property of congruence definition or postulate
Answers
The fill in the blanks are
1. 2PQ=PR ⇒ given
2. PQ+QR=PR ⇒ Segment addition postulate
3. 2PQ=PQ+QR ⇒Transitive property
4. PQ=QR ⇒ subtraction property
5.Q is the mid-point of PR ⇒ definition of mid- point.
What is a congruent ?
A congruence is a statement used in geometry that simply says that two objects are congruent, or have the exact same shape and size.
Given:
The given line segment PQR
2PQ=PR
Q is the mid point of PR.
According to given question we have
1. 2PQ=PR ⇒ given
2. PQ+QR=PR ⇒ Segment addition postulate
3. 2PQ=PQ+QR ⇒Transitive property
4. PQ=QR ⇒ subtraction property
5.Q is the mid-point of PR ⇒ definition of mid- point
Multiplication Postulate If equal quantities are multiplied by equal quantities, the products are equal.
Subtraction Postulate If equal quantities are subtracted from equal quantities, the differences are equal.
Addition Postulate If equal quantities are added to equal quantities, the sums are equal.
Therefore , the fill in the blanks are
1. 2PQ=PR ⇒ given
2. PQ+QR=PR ⇒ Segment addition postulate
3. 2PQ=PQ+QR ⇒Transitive property
4. PQ=QR ⇒ subtraction property
5.Q is the mid-point of PR ⇒ definition of mid- point.
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Can you help me please and thank yoh
Answers
Answer:
60, 3, 4, 150
Step-by-step explanation:
The top row you count by 1
On the second row you count by 30
a = 7cm, b = 14cm
Q1. Calculate the area and perimeter of the following ring where
(i)
Area of Ring:
(ii)
Perimeter of Ring:
Answers
Answer:
A =7 B=14
Step-by-step explanation:
AREA OF RING
PERIMETER OF RING
In this exercise, you’ll create a form that accepts one or more
scores from the user. Each time a score is added, the score total,
score count, and average score are calculated and displayed.
I ne
Answers
In this exercise, you’ll create a form that accepts one or more scores from the user. Each time a score is added, the score total, score count, and average score are calculated and displayed.
In order to achieve this, you will need to utilize HTML and JavaScript. First, create an HTML form that contains a text input field for the user to input a score and a button to add the score to a list. Then, create a JavaScript function that is triggered when the button is clicked.
To update these values, you will need to loop through the array of scores and calculate the total and count, and then divide the total by the count to get the average.
Finally, the function should display the updated values to the user. You can use HTML elements such as `` or `
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A procedure for approximating sampling distributions (which can then be used to construct confidence intervals) when theory cannot tell us their shape is:
a) residual analysis.
b) the bootstrap.
c) standardization.
d) least squares.
Answers
The procedure for approximating sampling distributions when the shape is unknown is the bootstrap method.
When theory cannot provide information about the shape of the sampling distribution, the bootstrap method is commonly used. The bootstrap is a resampling technique that allows us to estimate the sampling distribution by repeatedly sampling from the original data.
Here's how the bootstrap method works:
1. We start with a sample of data from the population of interest.
2. We randomly select observations from the sample, with replacement, to create a resampled dataset of the same size as the original sample.
3. We repeat this process numerous times, creating multiple resampled datasets.
4. With each resampled dataset, we calculate the statistic of interest (e.g., mean, median, standard deviation).
5. The distribution of these calculated statistics from the resampled datasets approximates the sampling distribution of the statistic.
By generating an empirical approximation of the sampling distribution through resampling, the bootstrap allows us to construct confidence intervals and make statistical inferences even when the underlying distribution is unknown or cannot be determined through theoretical means.
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = 2 x , y = 2 x2 , x = 4
Answers
The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
In this question,
The curves are y = 2/x, y = 2/x^2, x = 4
The diagram below shows the region enclosed by the given curves.
From the diagram, the limit of x is from 1 to 4.
The given curves are integrated with respect to x and the area is calculated as
\(A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx\)
⇒ \(A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx]\)
⇒ \(A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx]\)
⇒ \(A=2[lnx-\frac{1}{x} ] \limits^4_1\)
⇒ \(A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )]\)
⇒ A = 2[(1.3862-0.25) - (0-1)]
⇒ A = 2[1.1362 + 1]
⇒ A = 2[2.1362]
⇒ A = 4.2724 square units.
Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
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Danny has six orange colored shirts. This is 40% of the shirt he owns how many shirt does Danny own?
Answers
Answer:
Danny owns 15 shirts.
Step-by-step explanation:
We know
Danny has 6 orange-colored shirts; this is 40% of the shirt he owns.
How many shirts does Danny own?
We Take
(6 ÷ 40) x 100 = 15 shirts
So, Danny owns 15 shirts.
Answer: 15 shirts
Step-by-step explanation:
Step 1: We know that Danny has 6 orange shirts, which is 40% of the total number of shirts he owns.
Step 2: To find out the total number of shirts Danny owns, we can use the following formula:
Total number of shirts = (Number of orange shirts ÷ Percentage of orange shirts) × 100
Plugging in the values, we get:
Total number of shirts = (6 ÷ 40) × 100 = 15
Therefore, Danny owns a total of 15 shirts.
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Question Progress
The points A, B, C and D lie in order on a straight line.
AB BD = 2:3
AC: CD = 2:1
Work out AB: BC: CD
Give your answer in its simplest form.
Optional working
Answer:
D
Answers
The complete line ratio AB : BC : CD is 6 : 2 : 5
How to determine the complete ratio?From the question, we have the following parameters that can be used in our computation:
AB : BD = 2 : 3
AC : CD = 2 : 1
Rewrite them as
x ⇒ AB : BD = 2 : 3
y ⇒ AC : CD = 2 : 1
These ratios can be represented using the following equation
2x + 3x = 2y + y
Evaluate the sum
5x = 3y
Simplify
x = 3/5y
So, we have
AB : BC : CD
This gives
AB : CD - BD : CD
So, we have
2x : y - x : y
Solving further, we have
2 * 3/5y : y - 3/5y : y
Evaluate
6/5y : 2/5y : y
Multiply through by 5
6y : 2y : 5y
Divide through by y
6 : 2 : 5
Hence, the ratio is 6 : 2 : 5
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a straight line passed through the points (3,4) and (3,8). what is the question of the line?
Answers
Answer:
x - 3 = 0
Step-by-step explanation:
Click on this link, for I cant explain things very well :(
www.mathportal.org/calculators/analytic-geometry/two-point-form-calculator.php?val1=3&val2=4&val3=3&val4=8&rb1=gen
seven more than three times a number is 25 what is the number? please help asap thank u so much
Answers
Answer:
n = 10
Step-by-step explanation:
(10 * 3) + 7 = 37
Answer: 6
Step-by-step explanation:
With these type of problems, it is best to work backwards.
1. Because of the seven more, you subtract 7 from 25. This gives you 18.
2. Then it says three times, this means to divide by 3. 18/3 is 6
3. Your final answer is 6
Proving the answer is 6:
1. 3 \(*\\\) 6 = 18
2. 18 + 7 = 25
m to the power of 5 ×m to the power of 6 × n to the power of 11 over m to the power of 3 × n to the power of 5 × n
Answers
Step-by-step explanation:
\( \frac{( {m}^{5} \times {m}^{6} \times {n}^{11})}{ {m}^{3} \times {n}^{5} \times n} \\ = \frac{ {m}^{11} \times {n}^{11} }{ {m}^{3} \times {n}^{6} } \\ = {m}^{8} \times {n}^{5} \\ = {m}^{8} {n}^{5} \)
Answer:
\(\frac{m^5 \times m^6 \times n^{11}}{m^3 \times n^5 \times n^1}\)
Step-by-step explanation:
m to the power of 5 = m⁵
m to the power of 6 = m ⁶
n to the power of 3 = n³
n to the power of 11 = n¹¹
\(m^5 \times m^6 \times n^{11}\) over \(m^3 \times n^5 \times n^1\) = \(\frac{m^5 \times m^6 \times n^{11}}{m^3 \times n^5 \times n^1}\)
Simplified form:
\(m^{(5+6-3)} \times n^{(11 - 5- 1)} = m^8 \times n^{6}\)
Suppose a department contains 10 men and 15 women. a) How many ways are there to form a committee of 6 people from the department? Explain your answer. b) How many ways are there to form a committee of 6 people from the department, if the number of men in the committee is equal to the number of females in the committee? Explain your answer. c) How many ways are there to form a committee of 6 people from the department, if the number of men in the committee is less than the number of females in the committee? Explain your answer.
Answers
a) The number of ways to form a committee of 6 people from the department is 177,100.
b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.
c) The number of ways to form a committee of 6 people with more women than men is 91,455.
a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.
The number of ways to choose 6 people from a group of 25 is given by the combination formula:
C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100
Therefore, there are 177,100 ways to form a committee of 6 people from the department.
b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.
The number of ways to choose 3 men from 10 is given by the combination formula:
C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120
Similarly, the number of ways to choose 3 women from 15 is:
C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455
To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:
Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600
Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.
c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.
For 1 man and 5 women:
Number of ways to choose 1 man from 10: C(10, 1) = 10
Number of ways to choose 5 women from 15: C(15, 5) = 3,003
For 2 men and 4 women:
Number of ways to choose 2 men from 10: C(10, 2) = 45
Number of ways to choose 4 women from 15: C(15, 4) = 1,365
The total number of ways to form a committee with more women than men is the sum of these two cases:
Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)
= 10 * 3,003 + 45 * 1,365
= 30,030 + 61,425
= 91,455
Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.
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6 16 Next → Pretest: Scientific Notation Drag the tiles to the correct boxes to complete the pairs.. Particle Mass (grams) proton 1.6726 × 10-24 The table gives the masses of the three fundamental particles of an atom. Match each combination of particles with its total mass. Round E factors to four decimal places. 10-24 neutron 1.6749 × electron 9.108 × 10-28 two protons and one neutron one electron, one proton, and one neutron Mass 0-24 grams two electrons and one proton one proton and two neutrons Submit Test Particles F
Answers
We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:
1. 1.6744 × 10⁻²⁴: Two electrons and 0ne proton
2. 5.021 × 10⁻²⁴: Two protons and one neutron
3. 5.0224 × 10⁻²⁴: One proton and two neutrons
4. 3.3484 × 10⁻²⁴: One electron, one proton, and one neutron
How to match the particlesTo match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to 1.6726 × 10⁻²⁴ and one electron is equal to 9.108 × 10⁻²⁸.
To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;
1.6744 × 10⁻²⁴, we would
Add 2 electrons and one proton
= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴
= 1.6744 × 10⁻²⁴
The same applies to the other combinations.
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how do we forecast using data that has seasonality?
How can we control volatility in various time series models?
What is a simple moving average method?
Answers
To forecast using data that has seasonality, one commonly used method is seasonal decomposition of time series (STL). This method separates the time series data into three components: trend, seasonality, and residuals. By isolating the seasonal component, you can forecast future values by extrapolating the pattern observed in previous seasons.
Another approach is the use of seasonal autoregressive integrated moving average (SARIMA) models. SARIMA models are an extension of ARIMA models that incorporate seasonal patterns. These models capture both the trend and seasonality in the data and can be used to make forecasts.
To control volatility in various time series models, a common technique is to use a volatility model, such as the generalized autoregressive conditional heteroskedasticity (GARCH) model. This model estimates the volatility of the time series by incorporating past volatility and squared residuals. By modeling and forecasting the volatility, you can better understand and manage the potential fluctuations in the time series data.
A simple moving average method is a technique used to smooth out fluctuations and identify trends in time series data. It involves calculating the average of a fixed number of data points, often referred to as the window size or period. As new data becomes available, the oldest data point in the window is dropped, and the newest data point is included in the calculation. This process is repeated for each subsequent data point. The resulting moving average values can provide insights into the overall trend of the data, helping to identify patterns or changes over time.
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If you have 34 cookies and eat 7 plus 4/9 how much do you have?
Answers
Answer:
26 and 5/9 are left if you eat 7 and 4/9 of 34 cookies.
Step-by-step explanation:
Answer:
15 cookies
Step-by-step explanation:
34-7=27
eat 4/9 of remaining cookies means 27÷9×4= 12 more cookies are eaten
27 - 12 = 15
Can someone help me with this (photo attached)
Answers
Answer:
Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
To solve these problems you must use, Distributive Property.
What is Distributive Property?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
The Distributive Property was used to solve the following problems:
1. 2(4+9w)= 18w+8
2. 8(2w+4)= 16w+32
3. (-4w+1)3= -12w+3
4. -2(-5-w)= 2w+10
5. 2(-4-7)= 22
6. (10-2w)(-5) = 10w-50
(Hope this helps!
HELP HELP HELP HELP MEEE
Answers
and the range is (3,oo)
A bag contains 20 coloured marbles. Copy and
complete the table below to show the probability of
picking each colour at random and the number of
each colour marble in the bag. What is the
probability, as a percentage (%), of picking a purple
marble at random? How many purple marbles are in
the bag?
Colour
Yellow
Blue
Green
Purple
Probability
10%
15%
Number of marbles
6
Answers
Blue Probability = 30 %
Green No. of balls = 3
Purple Probability = 45 %
Purple No. of balls = 9
The coordinates of the point
3
10 of the way from A to B are
Answers
Using proportions, the coordinates of the point 3/10 of the way from A(-4,-8) to B(9,6) are: (-0.1, -3.8).
What is the missing information?The missing information is the graph containing points A and B, which is given at the end of the answer.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The coordinates of A and B are given as follows:
A(-4,-8), B(9,6).
For the point C 3/10 of the way, we have that:
C - A = 3/10(B - A).
The x-coordinate is found as follows:
x + 4 = 3/10(9 + 4)
x + 4 = 3 x 1.3
x = -0.1.
The y-coordinate is found as follows:
y + 8 = 3/10(6 + 8)
y + 8 = 3 x 1.4
y = -3.8.
The coordinates of the point 3/10 of the way from A(-4,-8) to B(9,6) are: (-0.1, -3.8).
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find y if the line through the points (-4,y) and (8,2) has a slope of -1/3
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Step-by-step explanation:
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An ellipse or hyperbola uses the general form ax2+cy2+dx+ey+f=0. solving for 5 unknowns (a, b, c, d, e, f) requires 5 equations, needs 5 points given. but if one of the coefficients is divided out (a or c), then only 4 coefficients remain and only 4 points are needed. x2+cy2+dx+ey+f=0 given 4 points on a vertical ellipse (3.75, 0), (0, 2.71), (1, -7), and (-1, -5.725). select the missing coefficients (answers have been rounded to the nearest tenth).
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the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.
To determine the missing coefficients in the equation x² + cy² + dx + ey + f = 0, we can use the given points on a vertical ellipse and substitute them into the equation. This will create a system of equations that we can solve to find the values of c, d, e, and f.
Let's substitute the given points into the equation:
For the point (3.75, 0):
(3.75)² + c(0)² + d(3.75) + e(0) + f = 0
14.06 + 3.75d + f = 0 -- Equation 1
For the point (0, 2.71):
(0)² + c(2.71)² + d(0) + e(2.71) + f = 0
7.35c + 2.71e + f = 0 -- Equation 2
For the point (1, -7):
(1)² + c(-7)² + d(1) + e(-7) + f = 0
1 + 49c + d - 7e + f = 0 -- Equation 3
For the point (-1, -5.725):
(-1)² + c(-5.725)² + d(-1) + e(-5.725) + f = 0
1 + 32.86c - d - 5.725e + f = 0 -- Equation 4
We now have a system of equations with four variables (c, d, e, f). By solving this system, we can find the missing coefficients.
Solving the system of equations using a numerical solver or by hand, we find the following approximate values:
c ≈ 0.5
d ≈ 0.7
e ≈ -1.6
f ≈ -9.9
Therefore, the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.
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Rewrite y = 2(1.06)9t to determine whether it represents exponential growth or exponential decay. then identify the percent rate of change. round each value to the nearest hundredth, if necessary.
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The equation y = 2(1.06)9t represents exponential growth because the base of the exponent is greater than 1. This means that as time (t) increases, the quantity y also increases. The percent rate of change for this exponential growth equation is approximately 6.06%, indicating the rate at which the quantity y is growing over time.
The equation y = 2(1.06)9t represents exponential growth because the base of the exponent, 1.06, is greater than 1. In exponential growth, the quantity increases over time.
To identify the percent rate of change, we can compare the initial value of y (when t = 0) to the value of y after a certain time interval.
When t = 0, the equation becomes y = 2(1.06)9(0) = 2(1.06)0 = 2(1) = 2.
Let's calculate the value of y after one time period, which is t = 1:
y = 2(1.06)9(1) ≈ 2(1.06) ≈ 2.1212.
The percent rate of change can be found by subtracting the initial value from the final value, dividing by the initial value, and then multiplying by 100.
Percent rate of change = ((final value - initial value) / initial value) * 100.
Using the values we calculated, the percent rate of change is approximately ((2.1212 - 2) / 2) * 100 ≈ 6.06%.
Therefore, the equation represents exponential growth with a percent rate of change of approximately 6.06%.
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I need help on this question
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Answer:
\(-\frac{21}{2} < x < -5\)
Solve the inequality
\(-3 < 2x+18 < 8\)
Separate compound inequalities into system of inequalities
\(\left \{ {{2x+18 > -3} \atop {2x+18 < 8}} \right.\\ 2x+18 > -3\ and\) \(2x-18 < 8\)
Rearrange variables to the left side of the equation
\(2x > -3-18\) \(2x < 8-18\)
Calculate the sum or difference
\(2x > -21\) \(2x < -10\)
Divide both sides of the inequality by the coefficient of variable
\(x > -\frac{21}{2}\) \(x < -\frac{10}{2}\)
Cross out the common factor
\(x < -5\)
\(x > -\frac{21}{2}\ and\ x < -5\)
Find the intersection
\(-\frac{21}{2} < x < -5\)
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Write the slope intercept form of the equation of each line given the slope and y intercept
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Answer:
Heyy, could you please take a screenshot? It'll be so much easier to see haha. Try Snipping tool if you have Windows, and Command + Shift + 4 for screenshot on Mac. Then I can answer.
Step-by-step explanation: