The distance of the triathlon, given the time Ingrid spent swimming, biking, and running, is 61.5 miles
How to find the distance?To find the distance of the triathlon, find the distance of the individual events which are the running, swimming, and biking. Then sum these distances up to find the triathlon distance that Ingrid ran.
The distance for swimming:
= Rate x Number of hours
= 3 x 0.5 hours
= 1.5 miles
The distance for biking:
= 12 x 3
= 36 miles
The distance for running:
= 6 x 4
= 24 miles
The triathlon distance is:
= 1.5 + 36 + 24
= 61.5 miles
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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%
-3(x-4)=-9(x-1) solving linear equations
-3(x-4)=-9(x-1)
-3x+12=-9x+9
-3x+9x=9-12
6x=-3
x= -3/6
x=-1/2
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 If you have 2/3 of your first 18-egg carton full, how many more eggs will fit in that
carton? What fraction card will you need to draw to fill the first carton exactly?
Answer:
6 eggs
Step-b6y-step explanation:
18 - (18× 2/3) = 6
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The melting point of a solid is the temperature at which is solid melts to become a liquid. The melting point of the element bromine is about 19°F. This is about 57°F more than the melting point of mercury. Which of the following equations can you use to find the melting point of mercury? What is the melting point of mercury?
x + 57 = 19
x - 57 = 19
x + 19 = 57
x + 19 = -57
Answer: A
Step-by-step explanation: If the melting point of Bromine is 19 degrees and the melting point of mercury is 57 degrees less than that then x (which is mercury's melting point) plus 57 degrees will equal 19.
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
**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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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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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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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
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.
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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Which number line represents the solutions to |x + 4 = 2?
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:
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
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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if f=72 when a=9 find a when f=56
Answer: just use the internet
Step-by-step explanation:
boom yo answer
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
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.
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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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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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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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:
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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directions in attachment!
The answers are 285 and 7392.
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!
7. A square pyramid has triangular faces, each with a base, of 8 inches and a height of 14 inches. The total surface area of the square pyramid is 288 in2. What is the area of the base of the square pyramid?
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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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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