The point where the line through (5, 2) with slope 4 crosses the vertical axis is (0, -18).
To do this, we can use the point-slope form of a line equation:
y - y1 = m(x - x1)
Here, (x1, y1) is the given point (5, 2) and m is the slope, which is 4. Let's plug in these values:
y - 2 = 4(x - 5)
Now, we need to find the point where the line crosses the vertical axis (y-axis). When a point is on the y-axis, its x-coordinate is 0. So, we will substitute 0 for x and solve for y:
y - 2 = 4(0 - 5)
y - 2 = -20
y = -20 + 2
y = -18
Therefore, the point where the line through (5, 2) with slope 4 crosses the vertical axis is (0, -18).
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If there are 280 6th graders and 200 7th graders, then how many more 7th graders are involved in the yearbook?
Using proportions, it is found that 8 more seventh graders are involved in the yearbook.
What is a proportion?
A proportion is a fraction of a total amount.
Researching the problem on the internet, it is found that 10% of the 6th graders and 18% of the 7th graders are on the yearbook, hence:
0.1 x 280 = 28 6th graders.
0.18 x 200 = 36 7th graders.
36 - 28 = 8
8 more seventh graders are involved in the yearbook.
Mike works a total of 59 hr per week at his two jobs. He makes $6 per hour at job A and $7 per hour at job B. If his total pay for one week is $374 before taxes, then how many hours does he work at each job?
Mike works 39 hours per week at Job A and 20 hours per week at Job B.
Calculating the work-rate of MikeWe need to formulate some expressions here.
Let:
Hours Mike works at Job A = x
Hours Mike works at Job B = y
We know that:
x + y = 59 ---------- equation 1
We also know that he makes $6 per hour at Job A, and $7 per hour at Job B, and his total pay is $374. So we can set up another equation based on his total pay:
6x + 7y = 374 --------- equation 2
Now we have two equations with two unknowns, which we can solve simultaneously.
Using substitution method:
solve for x in terms of y:
x = 59 - y
We can substitute this expression for x into equation 2:
6(59 - y) + 7y = 374
Simplifying and solving for y:
354 - 6y + 7y = 374
y = 20
So Mike works 20 hours per week at Job B. We can substitute this value for y into equation 1 to find x:
x + 20 = 59
x = 39
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A diver leaps off of cliff, modeled by the equation y =-16x^{2}-8x+120. When will the diver reach a height of 72 feet
The diver reaches a height of 72 feet after 1.5 seconds.
Given that, a diver leaps off of cliff, modeled by the equation,
y = -16x²- 8x +120.
We need to time taken by the diver to reach a height of 72 ft.
72 = -16x²- 8x + 120.
-16x²- 8x + 48 = 0
2x² + x - 6 = 0
Factorizing,
2x² + 4x -3x - 6 = 0
2x(x+2) -3(x+2) = 0
(2x-3)(x+2) = 0
x = -2, x = 1.5
Since, time cannot be negative so neglecting x = -2
Hence, the diver reaches a height of 72 feet after 1.5 seconds.
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Twenty-three greater than b is at least −276
Any value of b within this range would satisfy the original expression "23 > b ≥ -276".
The given expression is "23 > b ≥ -276". This means that b can take any value between -276 and 23, inclusive of -276 but not inclusive of 23.
To understand why this is the case, we can break down the expression into two parts: "23 > b" and "b ≥ -276".
The first part, "23 > b", means that b is less than 23. In other words, b can take any value that is less than 23. For example, b could be 22, 10, or even -100, as long as it is less than 23.
The second part, "b ≥ -276", means that b is greater than or equal to -276. This means that b can take any value that is greater than or equal to -276. For example, b could be -276, -200, or even 0, as long as it is greater than or equal to -276.
Putting these two parts together, we can see that b can take any value that is both less than 23 and greater than or equal to -276. This range of values for b is inclusive of -276 but not inclusive of 23, meaning that b cannot equal 23.
In numerical form, we can write the range of values for b as:
-276 ≤ b < 23
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Help me please and thank you
Answer:
2700
Step-by-step explanation:
im pretty sure that volume is length times width times height so
if u times these 3 numbers together its 2700
Find the smallest number n of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6. k=1 n=
The smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.
To find the smallest number of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6, we need to use the formula for the partial sum of a series. The partial sum of the given series up to n terms is:
S(n) = IM8 + 12e + 0.49(2^2) + 0.49(3^2) + ... + 0.49(n^2)
We want to find the smallest value of n such that the error between S(n) and the true value of the series is less than 10^-6. The error between S(n) and the true value of the series can be approximated by the absolute value of the next term in the series:
|an+1| = 0.49((n+1)^2)
So we need to find the smallest value of n such that:
|an+1| < 10^-6
0.49((n+1)^2) < 10^-6
(n+1)^2 < (10^-6)/0.49
n+1 < sqrt((10^-6)/0.49)
n < sqrt((10^-6)/0.49) - 1
n < 11.75
Since n must be a whole number, the smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.
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Zahra is a company specializing in high-end cosmetics. Its signature nail polish color is Soft Lilac. On a certain day, the company's factory had 5300 bottles of nail polish, and 1400 of those bottles were Soft Lilac. On that day, the inventory manager took a sample of 14 bottles of nail polish in the factory. She found that 3 of those bottles were Soft Lilac. For the inventory manager's sample, find and write with proper notation the population proportion and sample proportion of bottles that were Soft Lilac. Write the proportions as decimals (not percentages) rounded to two decimal places.
The population proportion (P) can be found by dividing the number of Soft Lilac bottles by the total number of bottles in the factory:
P = 1400 Soft Lilac bottles / 5300 total bottles
P ≈ 0.26 (rounded to two decimal places)
The sample proportion (p) can be found by dividing the number of Soft Lilac bottles in the sample by the total number of bottles in the sample:
p = 3 Soft Lilac bottles / 14 total bottles in the sample
p ≈ 0.21 (rounded to two decimal places)
So, the population proportion (P) of Soft Lilac bottles in Zahra's factory is approximately 0.26, and the sample proportion (p) of Soft Lilac bottles in the inventory manager's sample is approximately 0.21.
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5. 10 points Suppose that X (20,25) with mean 20 and variance 25. Please show all steps to find (a) P(19.6 < X < 20.4). (b) a so that P(x > a) 0.5517. (c) a so that P(X
a. A result between -0.08 and 0.08 has a probability of around 0.1562.
b. Using the standard normal distribution table the value of a is 19.4.
c. After using z-score to find the value of a, we got 28.2.
(a) To find P(19.6 < X < 20.4), we need to standardize the values and use the standard normal distribution table:
z1 = (19.6 - 20) / √(25) = -0.4 / 5 = -0.08
z2 = (20.4 - 20) / √(25) = 0.4 / 5 = 0.08
Using the standard normal distribution table, the probability of a value falling between -0.08 and 0.08 is approximately 0.1562. Therefore:
P(19.6 < X < 20.4) = 0.1562
(b) To find the value of a such that P(X > a) = 0.5517, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.5517:
P(X > a) = 1 - P(X ≤ a) = 0.5517
P(X ≤ a) = 1 - 0.5517 = 0.4483
Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.4483 is approximately -0.12. We can use this z-score to solve for a:
z = (a - μ) / σ
-0.12 = (a - 20) / 5
-0.6 = a - 20
a = 19.4
Therefore, a = 19.4.
(c) To find the value of a such that P(X > a) = 0.05, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.95:
P(X > a) = 0.05
P(X ≤ a) = 1 - 0.05 = 0.95
Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.95 is approximately 1.64. We can use this z-score to solve for a:
z = (a - μ) / σ
1.64 = (a - 20) / 5
8.2 = a - 20
a = 28.2
Therefore, a = 28.2.
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A. When José is done, they always fill the gas tank.
B. When Liam is done, they always fill the gas tank.
C. When they're done, José always fills the gas tank.
D. When he's done, he always fills the gas tank.
Answer:
C. When they're done, José always fills the gas tank.
Concentric circles are coplanar circles that have the same
Concentric circles are coplanar circles that have the same A. center.
What are concentric circles ?Concentric circles, a set of coplanar circles sharing the same center point, derive their name from the Latin word "concentricus," which translates to "having a common center."
Varied radii differentiate each concentric circle. If one circle has a smaller radius than another's, it is considered nested inside or simply, inside. Radius denotes the distance between the center point and edge of the circle perimeter.
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Options for this question include:
A. Center
B. Diameter
C. Circumference
D. Radius
True or false? -- A single, extremely large value can affect the median more than the mean. - Your answer: False True An extremely high or extremely low data value is called a(n)
The statement "A single, extremely large value can affect the median more than the mean" is True.
The median is the middle value when the data is arranged in ascending or descending order, and it is less affected by extreme values because it only considers the position of the value, not its actual magnitude.
On the other hand, the mean (average) takes into account the values themselves and can be heavily influenced by outliers. An extremely high or extremely low data value is called an outlier.
Outliers can skew the mean, pulling it towards their extreme value, while the median remains relatively unaffected. So the statement is True.
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A restaurant serves 10 different entrees, 6 of which contain meat. What is the ratio of vegetarian to non-vegetarian items?
Answer:
4/6 which is 2:3
Explanation:
the vegterian is 10-6=4
the non vegterian or eat meat is 6
and their ratio is 4/6
2:3
Goran swap 2 kilometers against the current in the same amount of time it took him to swim 8 kilometers with the current. The rate of the current was 3 kilometers per hour. How fast would Goran swim if there were no current?
Goran's swimming speed in still water is 5 km/h.
We have,
Let's call Goran's swimming speed in still water s.
When Goran is swimming against the current, his effective speed (relative to the ground) is:
= s - 3 km/h
(since the current is flowing against him),
And when he is swimming with the current, his effective speed is:
= s + 3 km/h.
The time it takes Goran to swim 2 kilometers against the current is the same as the time it takes him to swim 8 kilometers with the current.
Using the formula,
Time = distance/speed,
2 / (s - 3) = 8 / (s + 3)
Solve for s
2(s + 3) = 8(s - 3)
2s + 6 = 8s - 24
6s = 30
s = 5
Therefore,
Goran's swimming speed in still water is 5 km/h.
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Solve 2x 4 = 10.
O O
OA. x = 5
OB. x=3
OC. x = -3
OD. x = 7
Whats thé answer
The solution and value of x include the following: B. x = 3.
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
2x + 4 = 10.
By subtracting 4 from both sides of the equation, we have the following:
2x + 4 - 4 = 10 - 4
2x = 6
x = 6/2
x = 3.
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Complete Question:
Solve 2x + 4 = 10.
OA. x = 5
OB. x=3
OC. x = -3
OD. x = 7
use the method of your choice to determine the following probability. drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time. The probability of drawing three sevens is ______.
The probability of drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time is approximately 0.00012, or 0.012%.
To determine the probability of drawing three sevens in a row from a standard deck of cards without replacement, we can use the following method:
Step 1: Identify the total number of cards in a standard deck. A standard deck has 52 cards (13 ranks and 4 suits).
Step 2: Determine the number of sevens in the deck. There are 4 sevens (one from each suit).
The probability of drawing a seven from a standard deck of 52 cards is 4/52 or 1/13, since there are four sevens in the deck. After the first seven is drawn, there are 51 cards left in the deck, of which three are sevens. So the probability of drawing a second seven is 3/51. Similarly, after the second seven is drawn, there are 50 cards left in the deck, of which two are sevens. So the probability of drawing a third seven is 2/50.
Step 3: Calculate the probability of drawing the first seven. This would be the number of sevens divided by the total number of cards:
P(1st Seven) = 4/52
Step 4: After drawing the first seven, there are now 51 cards left in the deck and only 3 sevens remaining. Calculate the probability of drawing the second seven:
P(2nd Seven) = 3/51
Step 5: After drawing the second seven, there are now 50 cards left in the deck and only 2 sevens remaining. Calculate the probability of drawing the third seven:
P(3rd Seven) = 2/50
Step 6: To find the probability of all three events happening in a row, multiply the individual probabilities:
P(Three Sevens) = P(1st Seven) * P(2nd Seven) * P(3rd Seven) = (4/52) * (3/51) * (2/50)
Step 7: Calculate the result:
P(Three Sevens) = (4/52) * (3/51) * (2/50) = 0.0012 (approximately)
The probability of drawing three sevens in a row from a standard deck of cards without replacement is approximately 0.0012, or 0.12%.
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I need help with answering the screenshot
The function that is represented by the graph is -|x - 1| + 8.
Option A is the correct answer.
We have,
The graph of the function - |x - 1| + 8 can be obtained by applying a series of transformations to the graph of the absolute value function, y = |x|.
First, the expression x - 1 inside the absolute value brackets shifts the entire graph of y = |x| one unit to the right.
This means that the "V" shape of the absolute value function is centered at x = 1 instead of x = 0.
Next, the negative sign in front of the absolute value reflects the graph of y = |x| across the x-axis.
This means that the "V" shape is now pointing downwards instead of upwards.
Finally, the entire graph is shifted vertically upward by 8 units due to the constant term + 8.
This means that the lowest point of the "V" shape is at y = 8 instead of
y = 0.
Thus,
The function that is represented by the graph is -|x - 1| + 8.
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_____ is the tendency to emit repeatedly the same verbal or motor response to varied stimuli.
Answer:
perseveration
Step-by-step explanation:
The term you are looking for is "perseveration."
BC¯¯¯¯¯¯¯¯ ∥ AD¯¯¯¯¯¯¯¯
What type of angle pairs are form with the 75∘
angle and ∠2?
vertical angles
corresponding angles
adjacent angles
alternate interior angles
The angles 75° and ∠2 are alternate interior angles.
Option D is the correct answer.
We have,
From the figure,
55°, ∠3, and 75° forms a straight angle.
Alternate angles are pairs of angles formed when a transversal line intersects two parallel lines.
Alternate angles are equal in measure, which means they have the same angle degree value.
So,
75° and ∠2 are alternate angles.
Thus,
75° and ∠2 are alternate angles.
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Which expressions will help you find the surface area of this net? Select all that apply.
The expression that will help in finding the surface area of the net are
9 x 51/2 x 4 x 6What is surface area?The external surface area of three-dimensional objects is referred to as the surface area, and is generally calculated in square units.
Calculating the surface area of certain 3D shapes requires one to use different formulas. depending on the shapes
The shapes encountered here are
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pls answer this anyone
The values of angles in the diagram are ∠DAE = 53⁰, ∠DAE = 48⁰, ∠ACB = 102⁰, ∠ABC = 56⁰.
What is the value of the marked angles?
The value of angles is calculated as follows;
∠DAE = 90 - 37 (complementary angles add up to 90⁰ )
∠DAE = 53⁰
∠DBE = 90 - 42 (complementary angles add up to 90⁰ )
∠DAE = 48⁰
∠ACB = 180 - 78 (sum of angles on a straight line )
∠ACB = 102⁰
∠ABC = 180 - (22 + 102) (sum of angles in a triangle )
∠ABC = 56⁰
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Assume the characteristic polynomial of a matrix A is det(A –λ I) = (1 - λ)2(5 –λ ). If possible give concrete examples of such a matrix so that: (a) A is diagonalizable but not diagonal; (b) A is not diagonalizable if not possible wxplain why
a) A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.
b) A is not diagonalizable.
(a) A is diagonalizable but not diagonal: One possible example of such a matrix A would be:
A = [[1, 1], [0, 5]]
The characteristic polynomial of A is det(A –λ I) = (1 - λ)2(5 –λ), as given. The eigenvalues of A are λ1 = 1 and λ2 = 5, both of which have algebraic multiplicity 2. The eigenvectors corresponding to λ1 = 1 are [1, 0] and [1, 1], while the eigenvector corresponding to λ2 = 5 is [0, 1]. It can be verified that the eigenvectors are linearly independent and thus form a basis for R2. Therefore, A is diagonalizable.
However, A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.
(b) A is not diagonalizable: One possible example of such a matrix A would be:
A = [[1, 1], [0, 1]]
The characteristic polynomial of A is det(A –λ I) = (1 - λ)^2, which has a repeated eigenvalue of λ = 1. The eigenvectors corresponding to λ = 1 are [1, 0] and [0, 1], but they do not form a basis for R2 because they are linearly dependent. Therefore, A is not diagonalizable.
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A pallelogram has one angle that measures 35. What are the measures of the other angles in the parallelogram
Answer:
35 35 145 and 145
Step-by-step explanation:
35 times 2
= 70
70- 360
= 290
290÷2
= 145
35 35 145 145
If one angle of the parallelogram measures 35, the other angles would be 35, 145, and 145.
The sum total of the interior angles in a parallelogram is 360 degrees. Also, in a parallelogram, the interior opposite angles are equal. It is given that one angle measures 35 degrees. Its opposite angle would also be 35 degrees.
35 + 35 = 70.
We know that sum of interior angles is 360 degrees. So, 360 - 70 =290. 290 is the sum of the other interior opposite angles. So therefore each of these angles would be 290/2= 145 degrees.
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write an expression for the apparent nth term (an) of the sequence. (assume that n begins with 1.) 2, 9, 28, 65, 126,
Therefore, the apparent nth term of the expression is: aⁿ = 5n² - 3n - 2.
The given sequence is not an arithmetic or geometric sequence. However, we can notice that the sequence of differences between consecutive terms is an arithmetic sequence.
The sequence of differences is: 7, 19, 37, 61,...
To find the nth term of this sequence, we can use the formula for the nth term of an arithmetic sequence:
dn = a1 + (n-1) * d
where dn is the nth term of the sequence of differences, a1 is the first term of the sequence of differences, d is the common difference of the sequence of differences, and n is the index of the term we want to find.
So, we have:
dn = 7 + (n-1) * 12
Simplifying this expression, we get:
dn = 5n - 3
Now, we can use this formula to find the nth term of the original sequence. Let's call the nth term an:
an = an-1 + dn-1
where an-1 is the (n-1)th term of the original sequence and dn-1 is the (n-1)th term of the sequence of differences.
We know that a1 = 2 and d1 = 7, so we can use the above formula to find the next terms:
a2 = a1 + d1 = 2 + 7 = 9
a3 = a2 + d2 = 9 + 19 = 28
a4 = a3 + d3 = 28 + 37 = 65
a5 = a4 + d4 = 65 + 61 = 126
Therefore, the apparent nth term of the sequence is: aⁿ = 5n² - 3n - 2.
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pls help <333 (don’t mind the white part, it was wrong)
The length of MS is 10 cm and diameter of the circle is RS
Given that the midpoint of PQ is M
RM is 10 cm and PQ is 24 cm
We have to find the length of MS
As M is midpoint then RM=MS
MS = 10 cm
Now the diameter of the circle is RS because it passes through middle of the circle which is center O
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What is the greatest value in the data set
Answer:
Step-by-step explanation:
Maximum :)
Help! What is the answer to 43 and 5/12’s times 11?
476 and 1/12, In summary, the answer to 43 and 5/12's times 11 is 5713/12 or 476 and 1/12.
To solve this problem, we need to convert the mixed number 43 and 5/12 into an improper fraction. We can do this by multiplying the whole number (43) by the denominator of the fraction (12), and adding the numerator (5) to get the total number of twelfths:
43 x 12 + 5 = 521/12
Now, we can multiply this fraction by 11:
521/12 x 11 = 5713/12
To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1:
5713/12
This is the final answer. However, if we want to express it as a mixed number, we can divide 5713 by 12 to get the whole number part (476) and the remainder
(1). Therefore, the final answer can also be written as:
476 and 1/12
In summary, the answer to 43 and 5/12's times 11 is 5713/12 or 476 and 1/12.
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Suppose follows the standard normal distribution. Use the calculator provided, or that, to determine the value of c so that the following true P(2>c) 0.2643 Round your answer to two decimal places 0 X
The z-score for 0.7129 is approximately 0.55. The value of c is 0.55, rounded to two decimal places.
1. We're given P(2 > c) = 0.2643, which means the area under the standard normal distribution curve between 2 and c is 0.2643.
2. We'll use the z-table or a calculator with a standard normal distribution function to find the corresponding z-score for c.
3. To find the area to the left of c, we need to first find the area to the left of 2. The z-score for 2 is 0.9772 (from the z-table or using a calculator).
4. Now, subtract the given area (0.2643) from the area to the left of 2: 0.9772 - 0.2643 = 0.7129.
5. Look up the z-score corresponding to the area 0.7129 in the z-table, or use a calculator with the inverse standard normal distribution function. The z-score for 0.7129 is approximately 0.55.
6. Therefore, the value of c is 0.55, rounded to two decimal places.
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consider the results of a poll where 48% of 331 americans who decide to not go to college do so because they cannot afford it. calculate a 90% confidence interval for the proportion of americans who decide to not go to college because they cannot afford it.
The 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it can be calculated using a statistical formula. The formula for a confidence interval is: CI = p ± zsqrt((p(1-p))/n)
Where CI is the confidence interval, p is the proportion of interest (in this case, 0.48 or 48%), and z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.645 for 90% confidence), sqrt is the square root function, and n is the sample size (in this case, 331).
Plugging in the values, we get:
CI = 0.48 ± 1.645sqrt((0.48(1-0.48))/331)
CI = 0.48 ± 0.062
Thus, the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is (0.418, 0.542). This means that we can be 90% confident that the true proportion of Americans who decide not to go to college because they cannot afford it falls between 41.8% and 54.2%.
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Which of the following equations has infinitely many solutions?
A
2x + 3 = 5 + 2x
B
2x + 3 = 5 + 3x
C
3x - 5 = -5 + 3x
D
2x - 5 = -5 + 3x
A. 2x + 3 = 5 + 2x has infinitely many solutions because the variable terms cancel out, leaving the statement 3 = 3, which is always true, regardless of the value of x.
Un televisor costaba $1250 y al comprarlo nos han hecho un 20% de descuento ¿cuánto nos han descontado?
They discount you $250 from the television cost.
How to calculate how much did they discount?Discount is defined as a deduction from the usual cost of something.
Since the television cost $1250 and when you bought it they gave you a 20% discount. We can say:
discount = 20% of $1250
discount = 20/100 * $1250
discount = $250
Therefore, they discount you $250
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Question in English
A television cost $1250 and when we bought it they gave us a 20% discount. How much did they discount us?