Answers
Step-by-step explanation:
it was not clear if an average change rate would be sufficient, or if you needed an immediate change rate (as I also don't know if you covered derivatives already or not).
so, it would be helpful, if you could put a message to an answer that was not giving you what you need.
so, here now an answer for an immediate change rate (hopefully that is what you need) :
we have a right-angled triangle.
the direct line of sight (the direct distance between police and red car) is the Hypotenuse (the baseline opposite of the 90° angle).
the 50 ft and 180 ft are the legs.
Pythagoras gives us the length of the Hypotenuse :
Hypotenuse² = 50² + 180² = 2500 + 32400 = 34,900
Hypotenuse = sqrt(34900) = 186.8154169... ft
in general terms let's say x is the distance of the cop to the road, y is the distance on the road to the crossing point with the distance cop to road, and z is the line of sight distance between the red car and the cop (the Hypotenuse).
x² + y² = z²
now, the first derivative of distance is the change of distance = speed.
then dy/dt (= y') is how fast the car is traveling down the road. dx/dt (= x') is how fast the cop is traveling toward the road. and dz/dt (= z') is how fast the distance between the cop and the car is changing.
now, we take the derivative of our equation
x² + y² = z² with respect to time, variable by variable :
d(x² + y² = z²)/dt =
dx²/dx × dx/dt + dy²/dy × dy/dt = dz²/dz × dz/dt
that gives us the equation
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
x(dx/dt) + y(dy/dt) = z(dz/dt)
from the problem we know x (50 ft), y (180 ft), dz/dt (85 ft/s). we calculated z (the Hypotenuse = sqrt(34900), and since the cop is not moving, we know dx/dt = 0.
and we get
50ft×0ft/s + 180ft×(y') = sqrt(34900)ft×(85)ft/s
we solve for y' (the speed of the car on the road)
y' = sqrt(34900)×85/180 = 88.21839132... ft/s
≈ 88.22 ft/s
and now here the difference for an average change rate over the unrevealed of 1 second :
the radar measured the change of the distance (Hypotenuse) from 1 second ago to now.
so, 1 second ago, the distance was
186.8154169... + 85 = 271.8154169... ft
the 50 ft leg stays the same, but the 180 ft leg was (again via Pythagoras)
271.8154169...² = 50² + leg²
leg² = 271.8154169...² - 50² = 71,383.62088...
leg = 267.1771339... ft
so, the red car traveled
267.1771339... - 180 = 87.1771339... ft/s
as you can see, it is close, but there has to be a difference, as the average change rate is only an approximation to the immediate change rate.
Related Questions
SUPPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: Angle 1 = 32, Angle 2 = x + 29
COMPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: 54 + x = 90
COMPLEMENTARY ANGLE Find the value of x. Answer only. Given: Angle 1 = x, Angle 2 = 24 + 2x
Answers
Answer:
Given: Angle 1 = 32, Angle 2 = x + 29 ----- Answer is x = 119°
Given: 54 + x = 90 ----- Answer is x = 36°
Given: Angle 1 = x, Angle 2 = 24 + 2x ----- Answer is x = 22°
Step-by-step explanation:
1. Supplementary angle = 180°
Angle 1 = 32° Angle 2 = x + 29
Angles 1 + 2 = 180°
32° + x + 29° = 180°
32° + x = 180° - 29°
32° + x = 151°
x = 151° - 32°
x = 119°
2. Complementary angle = 90°
Given: 54 + x = 90
90 - 54 = x
x = 36°
3. Complementary angle = 90°
Given: Angle 1 = x, Angle 2 = 24 + 2x
Angles 1 + 2 = 90°
x + 24 + 2x = 90°
3x + 24 = 90°
3x = 90° - 24
3x = 66°
x = 66°/3
x = 22°
Hope it helps!
The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial lengths. The circuits carry the same current. Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest
solve correctly and I will pay you $100
Answers
The rank of the three circuits consisting of concentric circular arcs according to the magnitudes of the magnetic fields they produce at C, from least to greatest is (3), (2), (1).
We know that, the radial segments don't produce magnetic field at C, so consider arcs.
Assume that the current is counter clockwise and the magnetic field to be positive pointing out of the page.
Understand that, magnetic field at the center from an arc φ of radius R is [tex]\frac{{{\mu _0}i\phi }}{{4\pi R}}[/tex]
Therefore, for (1) :
[tex]\begin{gathered}\begin{array}{l}B = \frac{{{\mu _0}i\pi }}{{4\pi \left( {3r} \right)}} + \frac{{{\mu _0}i\pi }}{{4\pi r}}\\ \Rightarrow B = \frac{1}{3}\frac{{{\mu _0}i}}{r}\end{array}\end{gathered}[/tex]
For (2) :
[tex]\begin{gathered}\begin{array}{l}B = \frac{{{\mu _0}i\pi }}{{4\pi \left( {3r} \right)}} - \frac{{{\mu _0}i\pi }}{{4\pi r}}\\ \Rightarrow B = - \frac{1}{6}\frac{{{\mu _0}i}}{r}\end{array}\end{gathered} \\[/tex]
For (3) :
[tex]\begin{gathered}\begin{array}{l}B = \frac{{{\mu _0}i\pi }}{{4\pi \left( {3r} \right)}} - \frac{{{\mu _0}i\left( {\frac{\pi }{2}} \right)}}{{4\pi r}} - \frac{{{\mu _0}i\left( {\frac{\pi }{2}} \right)}}{{4\pi \left( {2r} \right)}}\\ \Rightarrow B = - \frac{5}{{48}}\frac{{{\mu _0}i}}{r}\end{array}\end{gathered}[/tex]
Therefore, the magnitude of the magnetic fields at C after arranging them in the order of least to greatest are (3), (2), (1).
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A group of 15 athletes participated in a golf competition. Their scores are below:
Would a dot plot or a histogram best represent the data presented here? Why?
A) Histogram, because a large number of scores are reported as ranges
B) Histogram, because a small number of scores are reported individually
C) Dot plot. because a large number of scores are reported as ranges
D) Dot plot, because a small number of scores are reported individually
Answers
Hello, I think the answer is D. Since the scores arent that huge of a gap, dot plot because small number scores are reported individually
Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Answers
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
5. Which of these statistics is used in basketball as an all-in-one rating of how well a player performs per minute they play?
O A. Wins above replacement (WAR)
O B. Field goal percentage (FG%)
O C. Double doubles (DD2)
OD. Player efficiency rating (PER)
Answers
Answer:
Player Efficiency Rating (PER)
Step-by-step explanation:
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is Player Efficiency Rating (PER).
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is the Player Efficiency Rating (PER). So, correct option is D.
PER is a widely used metric that quantifies a player's overall performance by taking into account various statistical categories and normalizing them based on playing time.
PER evaluates a player's contributions in areas such as points, rebounds, assists, steals, blocks, and turnovers. It considers both positive and negative statistical events and provides a single numerical value that represents a player's efficiency on the court. A higher PER indicates a more productive player.
On the other hand, Wins Above Replacement (WAR) is a metric commonly used in baseball to estimate the number of wins a player contributes to their team compared to a replacement-level player.
Field Goal Percentage (FG%) measures the accuracy of a player's shooting by calculating the percentage of successful field goal attempts. Double doubles (DD2) count the number of games in which a player achieves double-digit totals in two statistical categories.
Among the options listed, Player Efficiency Rating (PER) is specifically designed to assess a player's overall performance per minute played in basketball.
So, correct option is D.
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What is the value of 2 x² - 4 y when x = -4 and y = 16?
Answers
Answer:
-32
Step-by-step explanation:
2x ^ 2 - 4
2(-4) ^ 2 - 4(16)
32 - 64
-32
ABC ~ DFE , solve for X please help
Answers
Step-by-step explanation:
x+2 is to 4 as 28 is to 7
(x+2) / 4 = 28 / 7 <====solve for 'x'
x+2 = 16
x = 14
What gravitational force does the moon produce on the Earth if their centers are 3.88x108 m apart and the moon has a mass of 7.34x1022 kg?
Answers
The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
What is gravitational force?
Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.
The gravitational force that the moon produces on the Earth can be calculated using the formula:
[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]
where:
[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]
[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]
[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]
[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]
Substituting these values into the formula, we get:
[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]
Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
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can you help me to solve these two questions?
Answers
Case 1: The constant c of the piecewise function is equal to 1 / 7.
Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.
How to determine the value of a variable such that a piecewise function is continuous
A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:
g(a) = h(a)
Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7
c · a + 3 = c · a² - 3
c · (a² - a) = 6
c = 6 / (a² - a)
c = 6 / (7² - 7)
c = 6 / 42
c = 1 / 7
The value of the constant c is equal to 1 / 7.
Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5
b - 2 · a = - 150 / (a - b)
(b - 2 · a) · (a - b) = - 150
a · b - b² - 2 · a² + 2 · a · b = - 150
- b² + 3 · a · b - 2 · a² = - 150
b² - 3 · a · b + 2 · a² - 150 = 0
b² - 15 · b - 100 = 0
(b - 20) · (b + 5) = 0
b₁ = 20 or b₂ = - 5
The solution with the greater absolute value is b = 20.
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she works a 35
-hour week earning $17.10
an hour.
How much does she earn in one year? (Use 52
weeks in one year.)
Answers
Answer:
$31122.00
Step-by-step explanation:
We know
She works 35 hours a week, earning $17.10 an hour.
17.10 x 35 = $598.50 a week
How much does she earn in one year?
We Take
598.50 x 52 = $31122.00
So, she earns $31122.00 one year.
What is the constant of proportionality between the corresponding areas from Rectangle A to Rectangle B?
Rectangle A: area = 5 in²
Rectangle B: area = 125 in²
Responses
5
10
15
25
Answers
Answer:
its 5
Step-by-step explanation:
I did this question
There are N distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type i with probability P_i, i, .., N. Hence, P_1 + P_2 +... + P_N = 1. Let T denote the number of coupons one needs to select to obtain at least one of each type. Compute P(T > n).
Answers
If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.
Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:
P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)
By the principle of inclusion-exclusion, we can write:
P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.
This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.
In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.
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If cos is the third quadrant find sin
Answers
The value of sinθ = -[tex]\frac{7}{8}[/tex] using trigonometry.
Trigonometry: What Is It?One of the most significant areas of mathematics, trigonometry has a wide range of applications. Trigonometry is a field of mathematics that primarily focuses on the analysis of how a right-angle triangle's sides and angles relate to one another. Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the absent or unknown angles or sides of a right triangle. Angles in geometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently used in computations.
In this question,
sin²θ + cos²θ= 1
sin²θ + (-1/4)² = 1
sin²θ = 1- (1/8)
sinθ = ± √(7/8)
since, it is in the third quadrant,
sinθ= -[tex]\frac{7}{8}[/tex]
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State whether the triangles could be proven congruent as SSS or SAS Theorem.
Answers
Using SSS theorem of congruency in triangles, we can prove that in all the cases, each triangle is congruent to the other.
What do you mean by congruent triangles?Whether two or more triangles are congruent depends on the size of the sides and angles. A triangle's size and shape are consequently determined by its three sides and three angles. If the pairings of the respective sides and accompanying angles are equal, two triangles are said to be congruent. Both of these are the exact same size and shape. Triangles may satisfy a number of distinct congruence requirements.
The SSS criterion is also known as the Side-Side-Side criterion. This standard states that two triangles are congruent if the sum of the three sides of each triangle is the same.
Here in the question,
It is given that the two sides of each triangle are equal to the corresponding sides of the other triangle.
Now as two sides of a triangle is equal to the two sides of another triangle, it is obvious that he third side will be equal to the corresponding sides of the other triangle.
Now as per the SSS criteria, as all the sides are equal to the corresponding sides of the other triangle, the triangle are congruent.
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Andy has 4 red cards, 3 blue cards, and 2 green cards. He chooses a card and replaces it before choosing a card again. How many possible outcomes are in the sample space of Andy's experiment?
A) 18
B) 9
C)81
D)3
Answers
There are 81 potential outcomes in Andy's sample space.
What are the potential results?Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.
The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.
We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.
For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.
9 × 9 = 81.
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Solve for X, please help
Answers
Answer:
x = 6
Step-by-step explanation:
If 3 or more parallel lines are intersected by two or more transversals , the parallel lines divide the transversals proportionally.
here 3 parallel lines are intersected by two transversals , then
[tex]\frac{1+4x}{20}[/tex] = [tex]\frac{15}{27-15}[/tex]
[tex]\frac{1+4x}{20}[/tex] = [tex]\frac{15}{12}[/tex] ( cross- multiply )
12(1 + 4x) = 20 × 15 = 300 ( divide both sides by 12 )
1 + 4x = 25 ( subtract 1 from both sides )
4x = 24 ( divide both sides by 4 )
x = 6
write a quadratic function in standard form that passes through the points (-8,0) ,(-5, -3) , and (-2,0) .
F(x)=
Answers
A quadratic function in standard form that passes through the points [tex](-8,0), (-5,-3), and (-2,0)[/tex] is equals to the [tex]f(x) = (1/3)( x^{2} + 10x + 16)[/tex].
What are some examples of quadratic functions?f(x) = ax2 + bx + c, in which a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
How do you determine whether an equation is quadratic?In other terms, you have a quadratic equation if a times the squares of the expression after b plus b twice that same equation not square plus c equals 0.
[tex]f(x) = ax^{2} + bx + c ----(1)[/tex]
is determined by three points and must be [tex]a[/tex] not equal [tex]0[/tex]. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs [tex](-8,0), (-5,-3)[/tex], and [tex](-2,0)[/tex] and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point[tex]( -8,0), x = -8, y = f(x) = 0[/tex] in equation [tex](1)[/tex],
[tex]= > 0 = a(-8)^{2} + b(-8) + c[/tex]
[tex]= > 64a - 8b + c = 0 -------(2)[/tex]
Similarly, for second point [tex]( -5,-3) , f(x) = -3, x = -5[/tex]
[tex]= > - 3 = a(-5)^{2} + (-5)b + c[/tex]
[tex]= > 25a - 5b + c = -3 --(3)[/tex]
Continue for third point [tex](-2,0)[/tex]
[tex]= > 0 = a(-2)^{2} + b(-2) + c[/tex]
[tex]= > 4a -2b + c = 0 --(4)[/tex]
So, we have three equations and three values to determine.
Subtract equation [tex](4)[/tex] from [tex](2)[/tex]
[tex]= > 64 a - 8b + c - 4a + 2b -c = 0[/tex]
[tex]= > 60a - 6b = 0[/tex]
[tex]= > 10a - b = 0 --(5)[/tex]
subtract equation [tex](4)[/tex] from [tex](3)[/tex]
[tex]= > 21a - 3b = -3 --(6)[/tex]
from equation (4) and (5),
[tex]= > 3( 10a - b) - 21a + 3b = -(- 3)[/tex]
[tex]= > 30a - 3b - 21a + 3b = 3[/tex]
[tex]= > 9a = 3[/tex]
[tex]= > a = 1/3[/tex]
from [tex](5)[/tex] , [tex]b = 10a = 10/3[/tex]
from [tex](4)[/tex], [tex]c = 2b - 4a = 20/3 - 4/3 = 16/3[/tex]
So,[tex]f(x)= (1/3)( x^{2} + 10x + 16)[/tex]
Hence, required values are [tex]1/3, 10/3,[/tex] and [tex]16/3[/tex].
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Answer:
f(x) = (1/3)x² + (10/3)x + 16/3-------------------------------------
Given 3 points of a quadratic function and two of them lie on the x-axis:
(-8, 0) and (-2, 0)These two points are representing the roots of the function. With known roots we can show the function in the factor form:
f(x) = a(x - x₁)(x - x₂), where a - coefficient, x₁ and x₂ are rootsSubstitute the roots into the equation and use the third point with coordinates x = - 5, f(x) = - 3, find the value of a:
-3 = a(- 5 + 8)((-5 + 2)- 3 = a(3)(-3)3a = 1a = 1/3This gives us the function in the factor form:
f(x) = (1/3)(x + 8)(x + 2)Convert this into standard form of f(x) = ax² + bx + c:
f(x) = (1/3)(x + 8)(x + 2)f(x) = (1/3)(x² + 10x + 16)f(x) = (1/3)x² + (10/3)x + 16/3For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete.a. X= the number of unbroken eggs in a randomly chosen standard egg cartonb. Y= the number of students on a class list for a particular course who are absent on the first day of classesc. U= the number of times a duffer has to swing at a golf ball before hitting itd. X= the length of a randomly selected rattlesnakee. Z= the amount of royalties earned from the sale of a first edition of 10,000 textbooksf. Y= the PH of a randomly chosen soil sample g. X= the tension (psi) at which a randomly selected tennis racket has been strungh. X= the total number of coin tosses required for three individuals to obtain a match (HHH or TTT)
Answers
a. X= number of unbroken eggs in a standard carton. b. Y= number of absent students on first day of a course. c. U= number of swings before hitting a golf ball. d. X= length of a rattlesnake.
e. Z= royalties earned from selling a first edition of 10,000 textbooks. f. Y= pH of a soil sample. g. X= tension (psi) of a tennis racket. h. X= total coin tosses required for three individuals to get a match.
a. X can take on values 0, 1, 2, 3, 4, 5, 6, as there can be zero to six unbroken eggs in a standard egg carton. X is a discrete random variable.
b. Y can take on values 0, 1, 2, 3, ..., n, where n is the total number of students on the class list. Y is a discrete random variable.
c. U can take on values 1, 2, 3, .... U is a discrete random variable.
d. X can take on any positive real value, as the length of a rattlesnake can vary continuously. X is a continuous random variable.
e. Z can take on any non-negative real value, as the amount of royalties earned can be any non-negative amount. Z is a continuous random variable.
f. Y can take on any value between 0 and 14, as the pH of a soil sample can range from 0 to 14. Y is a continuous random variable.
g. X can take on any positive real value, as the tension at which a tennis racket has been strung can vary continuously. X is a continuous random variable.
h. X can take on values 3, 4, 5, 6, ... as there must be at least three coin tosses and the tosses must continue until a match is obtained. X is a discrete random variable.
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Divide 240g in the ratio 5 4 3
Answers
Step-by-step explanation:
240g divided in ratios.
divide 240g in the ratio 5:4:3
To divide 240g in the ratio 5:4:3, we need to determine the amount of each part of the ratio.
First, we need to find the total number of parts in the ratio, which is 5 + 4 + 3 = 12.
Next, we divide the total amount (240g) by the total number of parts (12) to find the value of one part:
240g ÷ 12 = 20g
Therefore, one part of the ratio is equal to 20g.
To find the amount of each part of the ratio, we can multiply the value of one part by the corresponding number in the ratio.
The amounts are:
5 parts: 5 × 20g = 100g
4 parts: 4 × 20g = 80g
3 parts: 3 × 20g = 60g
Therefore, to divide 240g in the ratio 5:4:3, we need 100g, 80g, and 60g for each part of the ratio, respectively.
Answer
100g , 80g , 60g
Step-by-step explanation:
Ratio:Ratio = 5 : 4 : 3
Let the unit share be 'x'.
So, three shares are 5x, 4x and 3x.
Total weight = 240 g
Total shares = 5x + 4x + 3x = 12x
Sum of all the shares equal to the total weight.
12x = 240g
x = 240 ÷ 12 = 20
The value of unit share is 20 g. From this we can find the weight of each share.
5x = 5 * 20 = 100g
4x = 4 * 20 = 80 g
3x = 3 * 20 = 60 g
Find the standard normal area for each of the following (round your answer to 4 decimal places)
Answers
b.0.0218
c.0.9321
d.0.3096
PLEASE HELPPPPP 30 POINTSSSS!
Answers
Answer:
the answer will be 117
Step-by-step explanation:
you need to multiply
The surface area of a globe in Mr.Patton’s classroom is about 452.39 square inches. Find its volume in cubic inches . Use 3.14 for pi. Round to the nearest whole number
Answers
The volume of the globe is 905 cubic inches, for the given surface area.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.
The volume of the globe is given as:
V = 4/3πr³
The surface area if given as:
SA = 4πr²
Substituting the values of the given SA we have:
452.39 = 4 * 3.14(r²)
r = 6.01
Now, substitute the value of r in the equation of volume we have:
V = 4/3(3.14)(6.01)³
V = 904.78.
Hence, the volume of the globe is 905 cubic inches, for the given surface area.
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Imagine that there is an urn containing 5 blue chips and 5 red chips where chips are of equal dimensions and all chips in the urn at a time are equally likely to be selected. Let
X
denote the total number of blue chips obtained when 3 consecutive chips are drawn from the urn without replacement. (a) (10 points) Compute the probability that
X=3
Answers
The probability that X = 3 is 1/12.
To compute the probability that X = 3, we need to consider all possible ways of drawing three chips and count the number of ways in which we obtain three blue chips.
The total number of ways of drawing three chips from the urn without replacement is:
10C3 = (10!)/(3!7!) = 120
This is because we need to choose 3 chips out of the 10 in the urn, and the order in which we draw them does not matter.
Now, we need to count the number of ways in which we can obtain three blue chips. Since there are 5 blue chips in the urn, the number of ways of choosing 3 blue chips out of 5 is:
5C3 = (5!)/(3!2!) = 10
Therefore, the probability of obtaining three blue chips is:
P(X = 3) = 10/120 = 1/12
Hence, the probability that X = 3 is 1/12.
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The probability that X which denotes the total number of blue chips obtained when 3 consecutive chips are drawn from the urn without replacement is 1/12.
To calculate the probability that X = 3, the first step is to consider all the possible ways in which three chips can be drawn and count the number of ways in which we obtain three blue chips.
The total number of ways of drawing three chips from the urn without replacement is:
¹⁰C₃ = (10!)/(3!)(7!) = 120
This is because we need to choose 3 chips out of the 10 in the urn, and the order in which we draw them does not matter. Now, we need to count the number of ways in which we can obtain three blue chips. Since there are 5 blue chips in the urn, the number of ways of choosing 3 blue chips out of 5 is:
⁵C₃ = (5!)/(3!)(2!) = 10
Therefore, the probability of obtaining three blue chips is:
P(X = 3) = 10/120 = 1/12
Hence, the probability that X = 3 is 1/12.
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Ribbon wands are made from strips of ribbon tied to sticks. Connie has 84 feet of red ribbon, 48 feet of blue ribbon, and 72 feet of white ribbon. She wants to cut the ribbons into equal lengths that are as long as possible so that no ribbon is wasted
How many pieces of each color will she have?
Answers
Answer
Connie can cut the ribbon into 12 foot pieces.
Step-by-step explanation:
For these problems we should find the GCF, which is 12.
Interpret the slope of this function in the context of the situation. Use complete sentences.
Jennifer is painting an office complex. One wing has a large reception area with several equal-sized offices. Before painting, she must put tape on the baseboards. The amount of tape needed is given by the equation, y=12x+25 where y is total number of meters of tape, and x is the number of offices.
Answers
The slope of the function is 12. Because of the slope, Jennifer will require 12 extra meters of tape for each additional office she needs to tape the baseboards in.
What is slope?A line's slope on a graph is its steepness or inclination. It may be derived from any two locations on a line by dividing the vertical change (rise) by the horizontal change (run). Positive, negative, zero, or undefinable slopes are all possible for lines. A line on a graph with a positive slope is growing as you travel from left to right, while one with a negative slope is declining. A line has a slope of zero when it is horizontal and a slope of infinity when it is vertical.
The given function is y = 12x + 25.
The standard equation of the line is given as:
y = mx + b
where, m is the slope.
Comparing the equation with the given equation the slope of the function is 12.
Because of the slope, Jennifer will require 12 extra metres of tape for each additional office she needs to tape the baseboards in. In other words, if more offices need to be painted, the amount of sellotape required also grows linearly.
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through: (2,5), slope = 3
Answers
The equation of the line passing through (2,5) with a slope of 3 is y = 3x - 1.
This question is incomplete, the complete question is:
What is the equation of line passing through: (2,5), and with a slope = 3?
What is the equation of the line with the given point and slope?The equation of a line in slope-intercept form is expressed as:
y = mx + b
Where m is the slope and b is the y-intercept.
Given that, the point (2, 5) and the slope of the line is 3.
We can use the point-slope form of the equation of a line to find the equation in slope-intercept form:
y - y1 = m(x - x1)
Where x1 and y1 are the coordinates of the given point ( 2,5 ) and m is slope 3.
Substituting the given values, we get:
y - y1 = m(x - x1)
y - 5 = 3(x - 2)
Expanding and rearranging, we get:
y - 5 = 3x - 6
y = 3x - 1
Therefore, the equation of the line is y = 3x - 1.
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What are the values of the interior angles?
Round each angle to the nearest degree.
A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º
B) m∠X = 120º, m∠Y = 15º, m∠Z = 30º
C) m∠X = 145º, m∠Y = 18º, m∠Z = 36º
Answers
We can see here the values of the interior angles will be: A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º.
What is interior angle?An interior angle is an angle created between two adjacent sides of a polygon. To put it another way, it is the angle created by two polygonal sides that have a shared vertex.
Sum of interior angles of a triangle = 180°
[tex]2p + \frac{1}{4} p + \frac{1}{2} p = 180[/tex]
11p/4 = 180°
p = 720°/11
m∠X = 2p = 2 × 720°/11 = 130.9 ≈ 131°
m∠Y = [tex]\frac{1}{4} p[/tex] = 1/4 × 720°/11 = 16.3 ≈ 16°
m∠Z = [tex]\frac{1}{2} p[/tex] = 1/2 × 720°/11 = 32.7 ≈ 33°
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a water park sold 1679 tickets for total of 44,620 on a wa summer day..each adult tocket is $35 and each child ticket is $20. how many of each type of tixkwt were sold?
Answers
Therefore , the solution of the given problem of unitary method comes out to be the attraction sold 943 child tickets and 736 adult tickets on that particular day.
What is an unitary method?It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.
Here,
Assume the attraction sold x tickets for adults and y tickets for kids.
Based on the supplied data, we can construct the following two equations:
=> x + y = 1679 (equation 1, representing the total number of tickets sold)
=> 35x + 20y = 44620 (equation 2, representing the total revenue generated)
Using the elimination technique, we can find the values of x and y.
When we divide equation 1 by 20, we obtain:
=> 20x + 20y = 33580 (equation 3)
Equation 3 is obtained by subtracting equation 2 to yield:
=> 15x = 11040
=> x = 736
When we enter x = 736 into equation 1, we obtain:
=> 736 + y = 1679
=> y = 943
As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.
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Workers are preparing an athletic field by mixing soil and sand
in the correct ratio. The table shows the volume of sand to mix
with different volumes of soil. Which statement is correct?
A For 1,425 m³ of soil, the workers should use 375 m³ of sand.
B The ratio of the volume of soil to the volume of sand is 1:4.
C A graph of the relationship includes the point (900, 225).
D The equation y = 4x models the relationship.
Answers
Option B: The ratio of the volume of soil to the volume of sand is 1:4.
Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.
Option D: The equation y = 4x models the relationship.
We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.
So, the correct statements are B and D.
What is a graph?In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.
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The table mentioned in the question has been attached below.
A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose: (a) 24 candies? (b) 24 candies with at least a piece of each flavor? (b) 24 candies with at least 2 cherry and at least 2 lemon?
Answers
The solution for question a), b) and c) are as follows. The number of ways to choose 24 candies is 20475. And the number of of ways to choose 24 candies with at least a piece of each flavor is 7700. Similarly, the total number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is 272.
(a) To choose 24 candies from 5 types of hard candies, we can use the stars and bars method. We need to distribute 24 candies among 5 types, where each type can have 0 or more candies.
We can represent this by 24 stars (*) and 4 bars (|) to separate the candies of different types. The number of ways to arrange these stars and bars is the same as the number of ways to choose 4 positions out of 28 to place the bars. Therefore, the number of ways to choose 24 candies is:
(28 choose 4) = 20475
(b) To choose 24 candies with at least a piece of each flavor, we can first choose 5 candies, one of each flavor, and then choose 19 candies from the remaining candies. The number of ways to choose 19 candies from 20 candies (excluding one candy of each flavor) is:
(19 + 4 - 1) choose (4 - 1) = 22 choose 3 = 1540
Therefore, the total number of ways to choose 24 candies with at least a piece of each flavor is:
5 * 1540 = 7700
(c) To choose 24 candies with at least 2 cherry and at least 2 lemon, we can use the inclusion-exclusion principle. Let A be the event that we choose at least 2 cherry, and let B be the event that we choose at least 2 lemon. Then the number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is:
P(A union B) = P(A) + P(B) - P(A intersect B)
To calculate P(A), we can choose 2 cherry and then choose 20 candies from the remaining 3 types, which is:
(2 choose 2) * (20 + 3 - 1) choose (3 - 1) = 22 choose 2 = 231
Similarly, P(B) is also 231.
To calculate P(A intersect B), we can choose 2 cherry, 2 lemon, and then choose 18 candies from the remaining 3 types, which is:
(2 choose 2) * (2 choose 2) * (18 + 3 - 1) choose (3 - 1) = 20 choose 2 = 190
Therefore, the total number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is:
2 * 231 - 190 = 272
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