Answer:
The equation of the parabola is y = x²/4
Step-by-step explanation:
The given focus of the parabola = (0, 1)
The directrix of the parabola is y = -1
A form of the equation of a parabola is presented as follows;
(x - h)² = 4·p·(y - k)
We note that the equation of the directrix is y = k - p
The focus = (h, k + p)
Therefore, by comparison, we have;
k + p = 1...(1)
k - p = -1...(2)
h = 0...(3)
Adding equation (1) to equation (2) gives;
On the left hand side of the addition, we have;
k + p + (k - p) = k + k + p - p = 2·k
On the right hand side of the addition, we have;
1 + -1 = 0
Equating both sides, gives;
2·k = 0
∴ k = 0/2 = 0
From equation (1)
k + p = 0 + 1 = 1
∴ p = 1
Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;
(x - 0)² = 4 × 1 × (y - 0)
∴ x² = 4·y
The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;
y = x²/4.
Ravi bought a pack of 30 biscuits. He ate a fifth of them on Thursday.He ate a third of the remaining biscuits on Friday How Many biscuits did he have left?
Answer:
if I'm not mistaking (please correct if I'm wrong) but I think he would have 16 left.
Step-by-step explanation:
you have to divide one-fifth of 30 which would get you 6, then divide one-third of 24 ( because 30 - 6 is 24) then total both fractions to get 14. then finally subtract 14 from 30 to get 16.
An account earns simple interest. Find the annual interest rate.
I=$35
P= $1000
t = 6 months
The annual interest rate is
Answer:
This is the answer $2100
Step-by-step explanation:
$35×$1000×6/100=2100
Estimate by rounding to nearest 100 5428 + 6378 = ?
The function ƒ(x) = −(x + 3)^2 − 4 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.
Answer:
Step-by-step explanation:
The second one I believe.
Determine if the two triangles are congruent. If they are, State how you know. NO LINKS!!!! Show your work. Part 2c
Answer:
2. Not enough information
4. Congruent SAS
4. Similar, not enough information to determine congruency.
Step-by-step explanation:
2. We only know one side and one angle are congruent, Not enough to determine congruency
4. We know two sides and the angle between are vertical angles and vertical angles are congruent. SAS is how the triangles are congruent.
6. The three angles are congruent which makes the triangles similar. We need to know a side if they are to be congruent
Deborah finds that that the theoretical probability of flipping "heads" on a fair coin was 50%. After she flipped the fair coin 100 times, she calculated that she flipped heads 45 times. what is the percent difference in theoretical and experimental probability
Answer: 5% if it’s bubble sheet then 0.05
Step-by-step explanation:
Probability of flipping heads=50%
Probability of flipping practically = 45/100
=45
So 50%-45% = 5%
Solve x^2+14x=15 by completing the square.
The answer to your question is x=1
Answer:
-15, 1
Step-by-step explanation:
See image below:)
The radius of a circle is 10 cm. Find its circumference in terms of \piπ.
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle "[tex]r[/tex]" = 10 cm.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]
Therefore, the circumference of the circle is 20 π cm.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
First and 2nd question is easier.
1) What is 3% of 0.80 and what is 7% of 0.40
2) what is 90$ of 3 and what is 40% of 24
Answer:
3% of 0.80 = 0.024
7% of 0.40 = 0.028
90% of 3 = 2.7
40% of 24 = 9.6
Step-by-step explanation:
help me this question
Answer:
Option B
Step-by-step explanation:
The length and breadth of a rectangular field are 312m and 186m respectively; correct to the nearest metres. Between what limits must the field's perimetre lie? (Write your final answer as an inequality)
Answer:
[tex] P \geq 1000 \; meters [/tex]
Step-by-step explanation:
Given the following data;
Length = 312 meters
Breadth = 186 meters
To find the perimeter of the rectangle;
Mathematically, the perimeter of a rectangle is given by the formula;
Perimeter = 2(L + W)
Perimeter = 2(312 + 186)
Perimeter = 2(498)
Perimeter = 996 meters
To the nearest meters, we have;
Perimeter = 996 ≈ 1000 meters
Let P represent the perimeter of a rectangular field.
900 < P > 1000
Therefore, [tex] P \geq 1000 \; meters[/tex]
Please help meeeeeee!!
Find x so that m || n. Show your work.
Solution:-Since m || n, 4x – 23 = 2x + 17 by the Converse of alternate exterior angles theorem.
Solve for x.
[tex]\sf{4x-23=2x+17}[/tex]
[tex]\sf{4x-2x-23=2x-2x+17}[/tex]
[tex]\sf{2x-23=17}[/tex]
[tex]\sf{2x-23+23=17+23}[/tex]
[tex]\sf{2x=40}[/tex]
[tex]\sf{\frac{2x}{2}={\frac{40}{2}}}[/tex]
[tex]\sf{x={\color{magenta}{20}}}[/tex]
========================#Hope it helps!
(ノ^_^)ノ
Shannon was born on 12/21/1982. How many eight digit codes could she make using the digits in her birthday?
============================================================
Explanation:
Ignoring the slashes, there are 8 digits here. If we could tell those '1's and '2's apart, then we'd have 8! = 40,320 different codes. The exclamation mark indicates a factorial.
However, the '1's and '2's are indistinguishable. We have to divide by a!*b! = 3!*3! = 6*6 = 36 to account for this.
The a! = 3! = 6 is from the fact we have 3 copies of '1'.
The b! = 3! = 6 is from the fact we have 3 copies of '2'
Dividing by 36 gets us (40,320)/36 = 1120
The scatter plot below shows the ages and heights of a baseball team. Each dot represents one player. What is the total
number of 12-year olds who are more than 60 inches tall?
A 3
B 7
C5
D 2
Answer:
D
Step-by-step explanation:
if each dot is one person then there are only 2 people that are 12 and that are more than 60in tall
Answer:
its 2 because it says how many are 12 years old and are taller than 60
Consider the following time series. t 1 2 3 4 5 yt 6 10 8 13 15
(a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data?
(b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. If required, round your answers to two decimal places. y-intercept, b0 = 4.1 Slope, b1 = 2.1 MSE = ????
(c) What is the forecast for t = 6? If required, round your answer to one decimal place. 16.7 I know how to do it all but the MSE.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
t __1 2 3 4 5
yt_ 6 10 8 13 15
Using technology to produce a linear model :
The linear model obtained shows a positive linear pattern exist for the time series data :
The parameters for the line that minimizes MSE for the then series is :
y = 2.1t + 4.1
Where, slope = 2.1 ; intercept = 4.1
The mean squared error :
Sum of squared estimate of error = 9.1
Mean squared error = √9.1
Mean squared error = 3.02
Forecast for t = 6
y = 2.1t + 4.1
y = 2.1*6 + 4.1
y = 12.6 + 4.1
y = 16.7
20 POINTS!!
Suppose that, based on a sample, the 95% confidence interval for the mean of
a population is (23,39). What was the mean of the sample?
A. 31
B. 37
C. 35
D. 33
Answer: 31
Step-by-step explanation: just took the test
i don’t get this plz help
9514 1404 393
Answer:
f(x) = x(x-1) does not have an inverse function
Step-by-step explanation:
As you know, a function must be single-valued. That is, it can only have one y-value for each x-value.
If the inverse relation is to be a function, the original function must have only one x-value for each y-value. In general, even-degree polynomials, such as quadratic equations, cannot satisfy this requirement. This is often described as "the horizontal line test." That is, if a horizontal line intersects the graph in more than one place, the inverse relation is not a function.
The attachment shows a horizontal line intersecting f(x) = x(x-1) in more than one place. The inverse of this relation is not a function.
[tex] \rm{f(x) = x(x - 1)}[/tex]
[tex] \\ [/tex]
evaluate the expression when f=6 12f+3
Answer:
75
Step-by-step explanation:
Substitute 6 for f
12f+3=
12*6+3=
72 + 3 = 75
Answer:
12f+3 = 75 when f = 6
Step-by-step explanation:
12f+3
Let f = 6
12*6+3
Multiply
72 +3
Add
75
Ryan orders a pizza with a 20 inch diameter and asks for a cheese stuff crust along its border . The cheese filled border measures blank inches
I ONLY HAVE 5 minutes HELP!!!
Alvarez has $650 deposited into his bank account. The account earns simple interest of 6,5% per year. No other money is added or withdrawn from the account
for a period of four years. What is the total amount of money in the account after four years?
$143
O $685.75
C $793
D 8805.24
Answer:
685.75
Step-by-step explanation:
650*0.055+650
Jane wants to add chocolate chips to her trail mix. A 3-pound bag of chocolate chips cost $3.22 . What is the unit price ?
Answer:
It would be 1.073 you can also rojnd ot to 1.07
Answer:
$1.07 per pound
Step-by-step explanation:
$3.22/3lb is about $1.07 per lb.
What is the best description of the data in the histogram
A The data is set symmetrical
B The data interval is four
C The data set has a peak
D The data set has a cluster
Soosie's Cookie Company had fixed costs of $1250 and variable costs of $4.25 per dozen gourmet cookies that were baked and packaged for sale. Write an equation that can be used to determine the total cost when x dozens of cookies are baked and sold. Then determine the total cost of baking and selling 85 dozen gourmet cookies.
Answer:
$1250.00 + (x)$4.25 =
Step-by-step explanation
So fixed costs are $1,250.00.....every dozen you bake add $4.25 to the costs, cook one dozen you have $1,250.00 plus $4.25 or a total of $1,254.25.
Cook 10 dozen and you add $45.25 = the $1,250.00 for a new total of $1,295.25.
help help help help help
Answer:
11.
Step-by-step explanation:
The scores 60-69 has two people. The scores 70-79 have 9 people. Both are lower or below 80.
Answer:
11
Step-by-step explanation:
Add the number of people in the 60-69 range ( 2) and the number of people in the 70-79 range (9) to get the number of people below 80
2+9 = 11
You roll a 6-sided die.
What is P(odd)?
Write your answer as a percentage.
%
Submit
Answer:
it is 50%
Step-by-step explanation:
>:( im doing ixl and im in paine but here is the answer ok
Find the area of the kite with diagonals a= 12 and b=9
A) 30
B) 72
C) 54
D) 108
maybe 108 is the answer.
A is a plane figure bounded by more than four straight lines.
Answer:
A plane figure with 4 sides is called a quadrilateral.
Step-by-step explanation:
A plane figure bounded by more than four straight lines is generally referred to as a polygon. A polygon is a closed two-dimensional shape formed by connecting multiple line segments. The line segments, also known as sides, should intersect only at their endpoints, forming vertices of the polygon.
Polygons can have various numbers of sides, and their names are typically based on the number of sides they possess. Some common examples include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), and so on.
However, when the statement specifies that the plane figure is bounded by "more than four" straight lines, it suggests that the figure in question is a polygon with more than four sides. The exact name or classification of the polygon would depend on the specific number of sides it possesses.
To know more about plane figure . here
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What’s the ratio of 20 to 3
Answer:
666.666666666667%
Step-by-step explanation:
Convert fraction (ratio) - 20 / 3 Answer: -666.666666666667%
15 POINTS! PLEASE HELP! WILL GIVE BRAINLIEST!
Which expression should you simplify to find the 90% confidence interval for a sample of 36 people with a mean of 64 and standard deviation of 4? O +2 A. 36 2. VOA O B. 64 +2 4 V36 O C. 64 +1.645. 4. V36 4 O D. 36 +1.645 V64 SUBMIT
Answer:
c
Step-by-step explanation:
i took the test and got it right
For 90% confidence interval for a sample of 36 people with a mean of 64 and standard deviation of 4 the answer is C. 64 +1.645. 4. V36.
What is confidence interval?A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence.
In statistics, it is commonly used to estimate the population mean based on a sample mean, standard deviation, and sample size.
The confidence level represents the probability that the true population parameter falls within the calculated interval.
The correct expression to find the 90% confidence interval for a sample of 36 people with a mean of 64 and standard deviation of 4 is:
64 ± 1.645(4/√36)
Simplifying the expression:
64 ± 1.645(4/6)
64 ± 1.645(0.6667)
64 ± 1.0967
The 90% confidence interval is (62.9033, 65.0967).
Therefore, the answer is C. 64 +1.645. 4. V36.
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A person must score in the upper of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of and a standard deviation of , what score must a person have to qualify for Mensa (to whole number)
Answer:
The person must score at least [tex]X = \mu + Z\sigma[/tex], in which Z has a p-value of [tex]1 - \frac{p}{100}[/tex], considering p the upper percentage the person must score, [tex]\mu[/tex] is the mean IQ score for the population and [tex]\sigma[/tex] is the standard deviation.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
What score must a person have to qualify for Mensa?
Score of at least X, given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]X - \mu = Z\sigma[/tex]
[tex]X = \mu + Z\sigma[/tex]
In which Z has a p-value of [tex]1 - \frac{p}{100}[/tex], considering p the upper percentage the person must score.