In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.
The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.
Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.
Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.
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Jen’s assignment is to read at least 85 pages of a novel. Jen has read 31 pages. How many pages p does Jen have left to read? Write an inequality that represents this situation. Then solve the inequality
Jen has 54 pages left to read to meet her assignment requirement.
The inequality that represents this situation is p ≥ 85 - 31
To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.
The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:
p = 85 - 31
p = 54
Therefore, Jen has 54 pages left to read.
To represent this situation with an inequality, we can use:
p ≥ 85 - 31
This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).
Solving for p:
p ≥ 85 - 31
p ≥ 54
This means that Jen must read at least 54 more pages to meet her assignment requirement.
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What is the y-intercept of the line
with the equation y = - 4x - 12
Answer:
-12 is the y intercept while your slope is -4
Step-by-step explanation:
Estimating the within-group variance. Refer to the previous exercise. Here are the cell standard deviations and sample sizes for cooking enjoyment: Find the pooled estimate of the standard deviation for these data. Use the rule for examining standard deviations in ANOVA from Chapter 12 (page 560) to determine if it is reasonable to use a pooled standard deviation for the analysis of these data.
In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.
According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.
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How many sides has a polygon if the sum of its
interior angles is 1440⁰
Answer:
10 sides
Step-by-step explanation:
We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:
S = (n - 2) x 180 degrees
If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:
1440 = (n - 2) x 180
Dividing both sides by 180, we get:
8 = n - 2
Adding 2 to both sides, we get:
n = 10
Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.
A hawk flying at 19 m/s at an altitude of 228 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation y = 228 − x^2/57 until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.
The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.
We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.
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we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?
Probability of D2 being sunny = 0.78.
On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.
Therefore, we need to find the chances that D2 is sunny.
There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.
Now, Let us find the probability of D2 being sunny.
We have the following possible cases for D2.
D1 = Sunny; D2 = Sunny
D1 = Sunny; D2 = Rainy
D1 = Rainy; D2 = Sunny
D1 = Rainy; D2 = Rainy
The probability of D1 being sunny is 0.9.
When a sunny day follows a sunny day, the probability is 0.8.
When a sunny day follows a rainy day, the probability is 0.6.
Therefore, the probability of D2 being sunny is given by the formula:
Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.
Therefore, the probability that D2 is sunny are 0.78 or 78%.
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HELP PLS combine the like terms 3x+5-x+3+4x
Answer:
3x, 4x | 5, 3
Step-by-step explanation:
a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution. what type of probability distribution did the teacher use?
The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.
What is the Probability distribution?The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.
The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.
A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.
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y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Answer:
Y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Step-by-step explanation:
To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.
y = x^2 + 7x - 3
y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)
y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)
y = (x + 7/2)^2 - 49/4 - 3
y = (x + 7/2)^2 - 61/4
So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).
What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.
what is Combination?In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.
The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:
[tex]nCk = n! / (k! *(n-k)!)[/tex]
where n! denotes the factorial of n, i.e., the product of all positive integers up to n.
by the question.
Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:
[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]
Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]
Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).
Since a_i >= 4 for i=1, we have:
[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]
Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:
[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]
This gives us:
[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]
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