The searchlight is 0.333 ft deep, with the concept of the parabola equation
We will be using the equation of parabola for calculating the width of the opening here the vertex to focus is 3, so p=3
x² = 4py, where y is the width
=>x² = 4*3*y
=>x² = 12y ,
=>y = x² /12
Since here the dpeth is 2 feet, been the parabola be symmetry, distributed in two equal parts, we get 4/2 = 2, the y axix must take (y,-2) and (y,2) now substituting the values we get
y = (2 ^ 2)/12
y = 1/3 ,Therefore the depth is equal to 0.333 ft.
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For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: f (x) = negative 9 x squared + 7 x Table A a b c up or down y-intercept -9 -7 0 down (0,0) Table B a b c up or down y-intercept 2 7 0 down (0,0) Table C a b c up or down y-intercept 9 7 0 down (0,0) Table D a b c up or down y-intercept -9 7 0 down (0,0) a. Table A c. Table C b. Table B d. Table D
Examining the function -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0
How to find the y interceptsWhere a parabolic curve opens up or down in this case depends on the sign on the coefficient of the x².
The coefficient of x² is a and in this function is -9
A negative coefficient leads to opening downwards while a positive coefficient will result to opening upwards
The y intercept
-9x² + 7x = 0
x(-9x + 7) = 0
x = 0
-9x + 7 = 0
-9x = -7
x = 7/9
the y intercept is 0 ad 7/9
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The probability of obtaining a head when a certain coin is flipped is about 0.65 Whi ch of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times? A. 0.14 B. 0.37 0.39 0.60 0.65
The probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times is 0.37
Given:
P = 0.65
1-P = 1-0.65 = 0.35
n = 25
x = 15
The number of favorable outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.
Favorable Results/Total Results = x/n, where Probability(Event)
using binomial distribution:
P(X = x ) = ⁿCₓ (P)ˣ (1-P)ⁿ⁻ˣ
∴ Heads obtained 15 or fewer times
P(X ≤ 15)
we use exceed formula:
P(X≤15) = BINOM DIST(15,25,0.65,FALSE)
= 0.3696920
≈ 0.37
Hence we get the required answer.
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Suppoe the original quantity i 175 and the new quantity i 126. Write an expreion that repreent the percent change. Find the percent change and expre it a a rational number
The percent change for the expression for the given rational number is 28%.
Define the term percent change?A quantity's percentage change is equal to the ratio of such difference between the quantity's current value and its starting value multiplied as 100. When a quantity's ultimate value is determined by increasing or decreasing a percentage of its original value, there is always an change in the quantity's percentage change (or percent change).As the stated question-
Original quantity = 175
New quantity = 126
Difference = Original quantity - New quantity
Difference = 175 - 126
Difference = 49
Percentage change = Difference/Original quantity x 100 %
Percentage change =49/175 x 100%
Percentage change = 28%
Thus, percent change for the expression for the given rational number is 28%.
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What is the slope of a line parallel to a line whose equation is 10x+12y=-120
The slope of a line parallel to the line having equation 10x+12y=-120 is -5/6.
What is the slope of a line parallel to another line?
Parallel lines are coplanar and they never intersect.
Slope is a measure of the angle of a line from the horizontal.
Since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.
According to the given question:
Given equation of line is 10x+12y=-120
Converting this to slope-intercept form we get
y = -5/6 x + 10
Clearly slope of this line is -5/6
Any line parallel to this line will have the same slope
Therefore the slope of a line parallel to the given line is -5/6
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A barn is 100 feet long and 40 feet wide (see figure). A cross section of the roof is the inverted catenary given below. Find the number of square feet of roofing on the barn. (Round your answer to the nearest whole number.)
The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
What is integration?
It is defined as the mathematical approach to calculating the smaller parts or components.
It is given that:
A barn is 100 feet long and 40 feet wide.
Find the first derivative of the given function:
After solving the above integration:
= 20(e - 1/e)
The roofing = 100(20(e - 1/e))
= 4701 square feet
Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
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assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of 9.6. if 144 people are randomly selected, find the probability that their mean blood pressure will be less than 125.
The probability that the mean blood pressure will be less than 125 is 0.9938
The mean of the pressure readings = 123
The standard deviation = 9.6
Total population = 144
The value is less than 125
The equation of the z-score is
z-score = (Observed value - Mean ) / (Standard deviation /[tex]\sqrt{N}[/tex])
Substitute the values in the equation
z-score = (125 - 123) / (9.6/[tex]\sqrt{144}[/tex])
= 2 / (9.6/12)
= 2 / 0.8
= 2.5
Using the statistical table
The probability of that their mean blood pressure less than 125
P(z < 2.5) = 0.9938
Therefore, the probability is 0.9938
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Make g the subject of the formula w=7- square root g
The value of g is g = w² - 14w + 49, according to the question.
What do you mean by formula?
A truth or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more values. When you are aware of the value of one quantity, you can use the formula to determine the value of the other. It facilitates speedy question resolution. Formulas are used in algebra, geometry, and other subjects to speed up and simplify the process of arriving at the result.
According to the given question,
We have :
w = 7 - √g
Firstly isolate the g,
w = 7 - √g
Do the opposite of PEMDAS, first subtract 7 from both sides,,
w (-7) = -√g + 7 (-7)
w - 7 = -√g
Now, multiply -1 (as -√g is the same as -1√g) to both sides
-1(w - 7) = √g
-1w + 7 = √g
To get rid of the square root, you must square both sides,
Note: -1w is the same as -w.
Note: you are squaring all the terms on the other side, not just one.
(-w + 7)² = (√g)²
g = (-w + 7)²
g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or g = (-w + 7)² )
Use the FOIL method (First, Outside, Inside, Last)
(-w)(-w) = w²
(-w)(7) = -7w
(7)(-w) = -7w
(7)(7) = 49
g = w² - 7w - 7w + 49
Then, simplify (combine all like terms):
g =w² - 7w - 7w + 49
g = w² - 14w + 49
Therefore, the value of g = w² - 14w + 49 .
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What type of pair of angles are∠2 and angle∠11 ?
The type of pair of angles that are∠2 and angle∠11 is an alternate interior angles.
What is an alternate interior angle?When a transversal intersects two coplanar lines, alternate interior angles are formed. They are on the inside of the parallel lines, but on the outside of the transversal.
Angles with the same size that occur on opposite sides of the transversal line are known as alternate angles. The following alternate angles are equal: By drawing a Z shape, we can frequently identify interior alternate angles: Alternate angles are classified into two types: alternate interior angles and alternate exterior angles.
To understand alternate interior angles, imagine a set of parallel lines and then a line intersecting them. The intersecting line is known as a transversal, and all of the angles formed by the parallel lines are known as interior angles.
Both angles are interior angles that lie alternately to each other on the transversal line r. Therefore, they are alternate interior angle.
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The dinner bill came to $72.48 and Julio tipped the waiter 15%. What is the total price of dinner?
Answer: $83.35
Step-by-step explanation:
Find 15% of 72.48 = 10.87
10.87 + 72.48 = 83.35
The variables a and b are proportional. When a=12 we
know b=3. What is the value of a when b=5?
O 17
9
20
O 14
Answer:
b = 20
Step-by-step explanation:
the variables a and b are proportional , so the equation relating them is
a = kb ← k is the constant of proportion
to find k use the condition a = 12 , b = 3
12 = 3k ( divide both sides by 3 )
4 = k
a = 4b ← equation of proportion
when b = 5 , then
a = 4 × 5 = 20
list three ways a rectangle and a square are different
Answer:
one way is that they both have four sides.
another way is that they both have straight lines.
and the other way is that they both have 4 corners.
Step-by-step explanation:
Answer:
According to the web: "A square has four equal sides. In a rectangle, the opposite sides are equal. The diagonals of a square bisect each other at 90°. The diagonals of a rectangle bisect each other at different angles."
Step-by-step explanation:
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
On a map of a park three inches represents twenty feet, how many inches would represent 12 feet?
Answer:
1.8 inches
Step-by-step explanation:
in a proof what is the reason that justifies this statement: segment bp is congruent to segment bp.
The necessary explanation is that segment BP is congruent to segment BP, which is the common side of both triangles.
Two figures or items are congruent in geometry if they have about the same size, or if one has the same shape and size as its mirror counterpart.
As seen in the illustration, segment BP and segment BP are congruent since segment BP is the common side of both triangles BPS and BPY.
As a result, the necessary explanation seems to be that segment BP is congruent to segment BP and that segment BP is the identical side of both triangles.
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what is the solution to f(x)=g(x) ? select each correct answer.
The solution to f(x) = g(x) is
x = 0
x = 1
What do you mean by a solution?
We can substitute a value, or values, for a variable (such as x), making the equation true and thus finding a solution. All values of x in the domain, such that f(x) = g, are the solutions if two functions, f, and g, both map to the same co-domain.
as in: x + 2 = 7.
5 + 2 = 7 is what we get when we substitute 5 for x.
Given that 5 + 2 = 7, x = 5 is a solution.
Solution Explained:
A set of values in the table that tell us what the values of each function f(x) and g(x) are for a given value for the variable "x" is already giving us a hint.
We can infer from the table that f(x) decreases when x>0 and moves in the opposite way when x0.
G(x) follows a distinct path; it grows as x increases and shrinks as x lowers.
As a result, there is not much room for equality between the two functions.
You can thus utilize the points shown in the table to begin your test.
f(0)= 0,25 ^ 0=1 since a number raised to 0 is always 0.
g(0)=-0.75 * 0 + 1 = 1
f(1)=0.25^1=0.25 since a number raised to 1 is always equals to itself
g(1)=-0.75*1+1=0.25
So f(x)=g(x), when x=1 and when x=0
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The tape diagram below represents 100%. What percent is represented by the shaded area?
Answer:
Below
Step-by-step explanation:
shaded area is 3 out of 4 or 3/4 which is .75 which represents 75%
A hot chocolate recipe calls for 2/3 cup of milk.Slade wants to make 1/2 of the recipe.How much milk should Slade use?
Answer: Slade should use 1/3 cup of milk
Step-by-step explanation:
2/3 divided by 1/2 = 1/3
In other words, if you have 2 of something and you give someone half, you would give them 1.
**WILL MARK BRAINLIEST AND GIVE 30 POINTS**
Mrs. Thomason and Mrs. Ardoin are kayaking in the bayou in the same direction.
a) Mrs. Ardoin is boating at a constant speed of 15 miles per hour. Write an expression that shows how many miles Mrs. Ardoin has gone after x hours.
b) Mrs. Thomason starting kayaking of an hour before Mrs. Ardoin. If Mrs. Ardoin has been kayaking for x hours, how long has Mrs. Thomason been kayaking?
c) Mrs. Thomason is kayaking at a constant speed of 9 miles per hour. Write an expression that shows how many miles Mrs. Thomason has gone after Mrs. Ardoin has been riding for x hours.
d) Use your expressions to find when Mrs. Thomason and Mrs. Ardoin will meet.
a) The expression that shows how many miles Mrs. Ardoin has gone after x hours is of: s(t) = 15t.
b) Mrs. Thomason has been kayaking for x + 1/3 hours.
c) The expression that shows how many miles Mrs. Thomason has gone after Mrs. Ardoin has been riding for x hours: s(t) = 9t + 3.
d) They will meet after half an hour.
How to define the linear functions?The linear functions for the position are defined as follows:
s(t) = vt + s(0).
In which the variables are given as follows:
v is the velocity.t is the time.s(0) is the initial position.Mrs. Ardoin is boating at a constant speed of 15 miles per hour, hence his equation is of:
s(t) = 15t.
Mrs. Thomason has been kayaking for a third of an hour more than Mrs. Ardoin, at a rate of 9 miles per hour, hence his initial position is of:
s(0) = 1/3 x 9 = 3 miles.
Thus the equation is of:
s(t) = 9t + 3.
They will meet when:
15t = 9t + 3
6t = 3
t = 0.5.
Hence after half an hour.
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Use the theorem in Sec. 77, involving a single residue, to evaluate the integral of f (z) around the positively oriented circle |z| 3 when intergral c f(z) dz, f(z) = (z^3(1-3z))/(1+z) (1+2z^4)
The integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi times the sum of the residues of the poles of f (z) inside the circle.
The poles of f (z) inside the circle are z = 0 and z = −1/2.
The residue at z = 0 is f (0) = 0.
The residue at z = −1/2 is f (−1/2) = −7/16.
Therefore, the integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi (−7/16) = −7πi/8.
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Please help! you have to find the product
Answer:
-4x^2 - 6x
Step-by-step explanation:
2x(-2x-3)
Use the distributive property to multiply 2x by -2x - 3.
-4x^2 - 6x
Rewrite 16a4b + 8ab3 using a common factor.
2a4b(8 + 4ab3)
4ab(4a3 + 8ab3)
8ab(2a4b + 8ab3)
8ab(2a3 + b2)
The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.
What is GCF?GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.
The given expression is,
16a⁴b + 8ab³
Simplify the expression, by factor method,
8 x 2 x a x a x a x a x b + 8 x a x b x b x b
The common term is 8ab,
8ab(2a³ + b²)
The required expression is 8ab(2a³ + b²).
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in how many ways can we seat 6 people at a round table if john and sam insist on sitting next to each other? (two seatings are equivalent if one is a rotation of the other.)
If John and Sam insist on sitting next to each other, there are 48 different ways we can make a round table seat six people.
What is permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Here,
There is no head of the tabel so the first person is just a place marker so there are really only 5 people whose positions matter.
But John and sam are tied together so thet are the equaivalent of one person.
so that is only 4 people.
4!*2 (because it could be john, sam or sam, john)
2*3*4*2 = 48 permutations
In 48 ways we can make seat 6 people at a round table if john and sam insist on sitting next to each other.
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a clinical sample of patients with anorexia nervosa is randomly assigned to receive either cognitive-behavioral or psychodynamic therapy. upon completion of treatment, all participants are exposed to three different types of everyday stressors at different times. after exposure to each stressor type, the amount of food consumed by participants is recorded. which is the correct classification of this design?
2x3 mixed factorial design is the correct classification of this design.
In the given question, we have to find which is the correct classification of this design.
Three subgroups can be identified within this clinical grouping, though there are no clear divisions between them. The first category includes instances that closely resemble anorexia nervosa or bulimia nervosa but fall short of the diagnostic criteria's cutoff point.
Cases where the characteristics of AN and BN occur in various combinations from those seen in the prototypic illnesses make up the second and largest class.
Those who suffer from binge eating disorder make up the third grouping.
So, 2x3 mixed factorial design is the correct classification of this design.
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The right question is given below:
Prove that x^3+15x^2+74x+120 is always divisible by 6. Please
It is true that the polynomial is divisible by 6
How to prove the division of the polynomial?From the question, we have the following polynomial that can be used in our computation:
Polynomial = x^3+15x^2+74x+120
Divisor = 6
Rewrite the given parameters as
P(x) = x³ +15x² + 74x + 120
x = -6
Substitute x = -6 in the equation P(x) = x³ +15x² + 74x + 120
P(-6) = (-6)³ +15(-6)² + 74(-6) + 120
Evaluate
P(-6) = 0
because the result is 0, the polynomial is divisible
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find a parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4x2 8x 9 y2 36(z 1)2
x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like coordinates.
Given,
In response to our inquiry:
Add "-9y²" to each side of the equation.
4x² + 9y² + -9y² + -1z² = 36 + -9y²
9y² + -9y² = 0 when equivalent phrases are combined.
4x² + 0 + -1z² = 36 + -9y²
4x² + -1z² = 36 + -9y²
Add "z²" to both sides of the equation.
4x² + -1z² + z² = 36 + -9y² + z²
Therefore,
x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like dimensions.
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I NEED HELP FAST!!!! Let s represent the number of games a baseball fan attends. Enter an inequality that represents all values of s for which buying a main box season ticket is less expensive than buying single-game main box tickets.
You are writing an article for your school newspaper about the Oakland Athletics. Season tickets go on sale next week and you have been assigned to write an article to help fans determine whether they should buy season tickets or single-game tickets based on their expected attendance at the games this season.
Buying a season ticket allows you to attend all 81 home games for a single price. Without a season ticket you have to pay for every single game that you attend.
Image result for Oakland Athletics Tickets Box Office
The table shows different ticket price options.
In this task you will answer six questions about the ticket price options and recommend which is best for fans. Be sure to show all your work for each item.
1. A season has 81 home games. If you purchase a season ticket in the bleacher section , what is the cost per game, in dollars for this ticket?
.2. Complete the table based on the single game ticket for seats in the Left field reserve section.
Step-by-step explanation:
The key role for CPS is to minimize stigma and be an ambassador for recovery. Describe a situation where you had to confront stigma
One serving of a fruit punch recipe serves 16 people.
Which of the following answer choices correctly lists the ordered pairs for 1, 2, 3, and 4 servings? (number of servings, number of people served)
This is the correct answer
(1, 16), (2, 32), (3, 48), (4, 64)
Now for part 2 Plot the ordered pairs from question 1. You can only plot one point at a time. Plot serving 1 below. The image is below. Please snip and sketch the image then edit the image and draw where the points go. Thanks :)
The required list of the ordered pairs for 1, 2, 3, and 4 servings as (1, 16), (2, 32), (3, 48), (4, 64).
What is an ordered pair?An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.
One serving of a fruit punch recipe serves 16 people.
As per the given question, the required solution would be as:
1 x 16 = 16 ⇒ (1, 16)
2 x 16 = 16 ⇒ (2, 32)
3 x 16 = 16 ⇒ (3, 48)
4 x 16 = 16 ⇒ (4, 64)
Thus, the required list of the ordered pairs for 1, 2, 3, and 4 servings as (1, 16), (2, 32), (3, 48), (4, 64).
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if f=72 when a=9 find a when f=56
Answer: just use the internet
Step-by-step explanation:
boom yo answer
Determine the slope of the line
A. 1/3
B. -1/3
C. 3/1
D. -3/1
Answer: C
Step-by-step explanation:
The graph is going up not going down so it can't be a negative slope and we can eliminate choices B & D. We know that the slope is rising over run, and we see that the y increase by 3, and x increase by 1, so the slope is 3/1.
Solve for x.
y=69
5x+15=y+2x-5
The solution of x in the equation is 79/3
How to determine the solution of x?From the question, we have the following parameters that can be used in our computation:
y = 69
5x + 15 = y + 2x - 5
Substitute y = 69 in the equation 5x + 15 = y + 2x - 5
So, we have
5x + 15 = 69 + 2x - 5
Collect the like terms
This gives
5x - 2x =69 - 5 + 15
Evaluate the like terms
This gives
3x = 79
Divide both sides by 3
x = 79/3
Hence, the solution is 79/3
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the capacities (in ampere-hours) of 10 batteries are 140, 136, 150, 144, 148, 152, 138, 141, 143, 151. (a) estimate the population variance σ2. (b) compute a 99 percent two-sided confidence interval for σ2.
The population variance of the capacities is 30.76
the capacities (in ampere-hours) of 10 batteries are 140, 136, 150, 144, 148, 152, 138, 141, 143, 151.
The number of observations n = 10
mean = (x₁ + x₂ + x₃.....x₁₀)/10
mean = (140 + 136 + 150 + 144 + 148 + 152 + 138+ 141 + 143 + 151)/10
mean = 1443/10 = 144.3
variance = ∑(x - mean)²/(n - 1)
variance = ((140 - 144.3)² + (136 - 144.3)² + (150 - 144.3)² + (144- 144.3)² + (148 - 144.3)² + (152 - 144.3)² + (138 - 144.3)² + (141-144.3)² + (143 - 144.3)² + (151 - 144.3)²)/(10 - 1)
variance = 276.9/9 = 30.76
Therefore, the population variance of the capacities is 30.76
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