The equation of the parabola with vertex (5, -3) and passing through (6, 1) in vertex form is y = [tex]4(x - 5)^2 - 3.[/tex]
To write the equation of a parabola in vertex form, we use the formula:
y = [tex]a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola. Given the vertex (5, -3) and a point (6, 1) the parabola passes through, we can plug these values into the equation to find a.
For the point (6, 1):
[tex]1 = a(6 - 5)^2 - 3[/tex]
[tex]1 = a(1)^2 - 3[/tex]
4 = a
So, the equation of the parabola in vertex form is:
y = [tex]4(x - 5)^2 - 3[/tex]
Three boys share 28 toy cars equally. How many cars did each boy get and how many were left over
A microwave is placed on top of two boxes. One box is 2 feet 5 inches tall the other box is 3 feet 11 inches tall and the other microwave is 3 feet 3 inches tall how tall are they combined?
Draw a garden with up to 5 rows and that has the same number of flowers in each row . Then two equation that match your array .
A random variable x takes four possible values, 0, 2, a, and b, where a and b are unknown numbers. if pr[x = 0] = 0.2, pr[x=2] = 0.4, pr[x = a] = 0.3, e[x] = 2.8 and it is the case that a + b = 6, what is the missing value of a ?
a.-1.0
b.5.0
c.7.0
d.cannot be determined without more information
e.none of the above
Final answer:
The missing value of the random variable X can be determined by solving the equation e[x] = 2.8 and substituting the known values. By solving the equation, we find that the missing value is c. 7.
Explanation:
a. In words, X = A random variable that takes four possible values: 0, 2, a, and b.
b. X~ A missing value that represent an unknown number for the random variable X.
c. In words, X = The missing value of the random variable X, denoted by a.
d. X A missing value that we need to determine.
In this case, the missing value of a can be found by substituting the known values into the equation a + b = 6. Since b = 6 - a, we can substitute this expression into the equation e[x] = 2.8 and solve for a. From the equation, we get 0.2(0) + 0.4(2) + 0.3(a) + 0.3(6 - a) = 2.8.
Solving this equation gives us a = 7. Therefore, the missing value of a is 7, so the correct answer is c.
Fractions EXPLAIN your answer.
What is the next letter a,z,e,b,I,y,o
which of the following represents the factorization of the trinomal below
Anjali went to Citizens Bank and borrowed $7,000 at a rate of 8%. The date of the loan was September 20. Anjali hoped to repay the loan on January 20. Assuming the loan is based on ordinary interest, Anjali will pay back how much interest on January 20? A. $187.18 B. $187.17 C. $189.78 D. $188.22
Answer:
$189.78
Step-by-step explanation:
"The computation of the interest on January 20 is shown below:
= Principal × interest rate × number of days ÷ total number of days in a year
= $7,000 × 8% × 122 days ÷ 360 days
= $7,000 × 8% × 0.338
= $189.78
The 122 days are calculated below:
September - 10 days
October - 31 days
November - 30 days
December - 31 days
January - 20 days
Total - 122 days
And we assume the 360 days in a year"
Don James wants to invest $55,000 to earn $6260 per year. he can invest in B-rates bonds paying 14% per year or in a certificate of Deposit (CD) paying 8% per year. How much money should be invested in each to realize exactly $6260 in interest per year?
rob cuts a 15-foot wire into 8 equal pieces.about how long is each piece ?
If p(a) = 0.25 and p(b) = 0.65, assuming independence of events, then p(a and
b.is:
The Independent events is 0.1625.Events A and B are considered independent if the likelihood of each event's occurrence is unaffected by the occurrence of the other.
Find the independent events?P(A/B) is equal to P(A.B)/P(B) by definition (A). P(A) = P(B) / P(B) (as A, B are Independent events).
Events A and B are considered independent if the likelihood of each event's occurrence is unaffected by the occurrence of the other. P(A) = P(AB) = 1/2, which suggests that the likelihood of event A occurring has not changed as a result of the occurrence of event B.
P(0.25) = P(0.25 * 0.65) = 1/2
P(0.25) = 0.1625.
The Independent events is 0.1625 .
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Suppose f−1 is the inverse of a differentiable function f and f(4) = 0, f′(4) = 1. find (f−1)′(0).
simplify the complex fraction. 9/y/6/y-7
Sam is a waiter at a local restaurant where he earns wages of $7 per hour. Sam figures that he also earns about $5 in tips for each person he serves. Sam works 6 hours on a particular day.
Answer:
y=5x+42
Where y is the money he earns and x is the number of person he serves.
Step-by-step explanation:
Let the number of person he serves =x
It is given that he earns $5 as tip for each person he serves.
Hence total tip earned for serving x person=5x
His fixed wages are $7 per hour and he works for 6 hours a day. Hence his wages per day are $7*6 =$42
Hence total money earned for a day , say y can be represented as
y=5x+42
one quart or one gram is greater
given the rectangle below, which of the following transformations will map the figure onto itself?
What is the y-intercept of the line given by the equation y = 5x - 21?
To find the y-intercept of y = 5x - 21, identify the constant term of the equation, which is -21, indicating the y-intercept is -21.
The y-intercept of the line given by the equation y = 5x - 21 can be found by analyzing the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Comparing the equation y = 5x - 21 with y = mx + b, we see that the y-intercept is -21 (b = -21).Therefore, the y-intercept of the line y = 5x - 21 is -21.what is x in _-18x−45=-12_
justin sold 300 liter of soda at a baseball game.how much is this in milliliters?
Answer:
300,000 mililiters
Step-by-step explanation:
Remember that in international system the convertions are really easy because they are done 10 by 10, so from liters to mili, there are 3 spots, 1000, so there are 1000 mili-liters in a liter, so you just need to multiply the 300 liters of soda by 1000, which is 300,000 mililiters and that is what Justin sold at the baseball game in mililiters.
Find all the local maxima, local minima, and saddle points of the function
Final answer:
To find local maxima, minima, and saddle points, find critical points using the first derivative test and then apply the second derivative test.
Explanation:
To find the local maxima, local minima, and saddle points of a function, we first need to find the critical points. These are the points where the derivative of the function is either zero or undefined. To check whether each critical point is a local maxima, local minima, or saddle point, we use the second derivative test.
The second derivative test states that if the second derivative is positive at a critical point, then the point is a local minimum. If the second derivative is negative, then the point is a local maxima. If the second derivative is zero, the test is inconclusive.
By applying the second derivative test to each critical point, we can determine whether it is a local maxima, local minima, or saddle point.
Solve the system of linear equations. separate the x- and y- values with a coma. 20x=-58-2y
17x=-49-2y
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 20 miles per hour faster than the westbound train. If the two trains are 750 miles apart after 5 hours, what is the rate of the eastbound train?
east bound train = x
westbound train = x-20 ( 20 miles slower than east bound)
5x + 5(x-20) = 750
5x +5x -100=750
10x -100 = 750
10x =850
x = 850/10 = 85
east bound train is 85 mph
west bound train is 85-20 = 65 mph
check: 85*5 = 425
65*5 = 325
325+425 = 750
A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck’s revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? A) 77 B) 93 C) 99 D) 105
Elspeth knows that PI r=9.42cm. What would she need to do to find the circumference?
The answer would be A! :)
What is the common ratio for the geometric sequence? 54,36,24,16... Enter your answer in the box.
The common ratio of the geometric sequence is: 2/3.
Common Ratio of a Geometric Sequence
Common ratio, r = a term divided by the consecutive term in the series.
Given the geometric sequence, 54,36,24,16...
common ratio (r) = 16/24 = 2/3.
24/36 = 2/3.
36/54 = 2/3.
Therefore, the common ratio of the geometric sequence is: 2/3.
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Find the limit, if it exists. (if an answer does not exist, enter dne.) lim (x, y) → (0, 0) x4 − 20y2 x2 + 10y2
The limit of the expression as (x, y) approaches (0, 0) does not exist.
Explanation:To find the limit as (x, y) approaches (0, 0) of the expression \(\frac{x^4 - 20y^2}{x^2 + 10y^2}\), we can try approaching the limit along different paths. Let's consider approaching along the x-axis (y=0) and along the y-axis (x=0) separately.
Approaching along the x-axis: \(\lim_{{(x, 0) \to (0, 0)}} \frac{{x^4 - 20(0)^2}}{{x^2 + 10(0)^2}} = \lim_{{(x, 0) \to (0, 0)}} \frac{{x^4}}{{x^2}} = \lim_{{(x, 0) \to (0, 0)}} x^2 = 0.
Approaching along the y-axis: \(\lim_{{(0, y) \to (0, 0)}} \frac{{(0)^4 - 20y^2}}{{(0)^2 + 10y^2}} = \lim_{{(0, y) \to (0, 0)}} \frac{{-20y^2}}{{10y^2}} = \lim_{{(0, y) \to (0, 0)}} -2 = -2.
Since the limit approaches different values along different paths, the limit does not exist.
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Find the probability that the mean annual preciptiation will be between 32 and 34 inches. variable is normally distributed
Choose the true statement about the graph of x > -3.
closed circle on -3 and all numbers to the right shaded
open circle on -3 and all numbers to the right shaded
open circle on -3 and all numbers to the left shaded
Answer:
open circle on -3 and all numbers to the right shaded
Mrs Rivera baked 112 cookies there are 28 students in her class how many cookies will each student receive
Each student will receive 4 cookies.
Explanation:To find out how many cookies each student will receive, we need to divide the total number of cookies by the number of students. In this case, Mrs. Rivera baked 112 cookies and there are 28 students, so we can divide 112 by 28 to find the answer.
Divide 112 by 28: 112 ÷ 28 = 4Therefore, each student will receive 4 cookies.Learn more about cookies divided among students here:https://brainly.com/question/34263620
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A random sample of is selected from this population. find the probability that the sample mean is greater than 2.1 but less than 2.5.