Here is a tree diagram to represent the sample space of Jill tossing a coin three times:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
What is sample space?The concept of the sample space is fundamental to the calculation of probabilities because it defines the set of all possible outcomes that we are interested in measuring the likelihood of. By specifying the sample space, we can define events (subsets of the sample space) and assign probabilities to those events.
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What is the area of one of the bases,b, of the prism b=_in2
Answer: 6
Step-by-step explanation:
Therefore, area of the base 'B' of given rectangular prism is equal to 6 in².
Answer:
Step-by-step explanation:
B= area of the triangle 1+area of triangle 2
(1/2*3*1)+(1/2*2*1)
=1.5+1
=2.5
Describe the following function
The transformation in the function y = -1/3f(x + 4) - 5 is described below
Describing the transformation in the functionFrom the question, we have the following parameters that can be used in our computation:
y = f(x)
The transformed function g(x) is given as
y = -1/3f(x + 4) - 5
The sequence of transformation on the transformed function is as follows
Horizontal shift to the left by 4 unitsVertical stretch by a factor of 1/3Reflection across the x-axisLastly, vertical shift down by 5 unitsRead more about transformation at
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(A) 0
(B) 1
2
(D) 3
Si un garçon peut courir une distance de 10 mètres pendant qu'une voiture en parcourt
0, combien de mètres le garçon pourra-t-il courir pendant que la voiture parcourt 66 mètres?
(A) 12
(B) 90
(C) 22
(D) 25
10 x = 30
Une équipe d'ouvriers fabriquaient 1,000 uniformes par semaine. La production ayar
té augmentée de 20%, chaque ouvrier se vit obligé de confectionner 50 uniformes de plus
Combien y avait-il d'ouvriers dans cette équipe?
(A) 4
(B) 15
(C) 20
110
(D) 24
Question 2 (2 points)
In the circle below, D is the center and segment AC is the diameter.
What is the measure of ZADC?Blank 1:
Blank 2
What is the measure of ZABC?
The measure of ∠ADC is equal to 180 degrees.
The measure of ∠ABC is equal to 90 degrees.
What is a circle?In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.
In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.
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A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
C(t)=18(0.91)t
The initial temperature of the soda is 18 degrees Celsius.
Its temperature after 20 minutes is 2.73 degrees Celsius.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value, initial value, or y-intercept.x represents time.b represents the rate of change.When time, t = 0, the initial value can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]
C(0) = 18(1)
C(0) = 18 degrees Celsius.
When time, t = 0 = 20, the temperature can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]
C(20) = 2.73 degrees Celsius.
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Complete Question:
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
[tex]C(t)=18(0.91)^{t}[/tex]
Find the initial temperature of the soda and its temperature after 20 minutes?
The parent function f ( x ) = 3 √ x is transformed to g ( x ) = 2 f ( x − 3 ) Which is the graph of g ( x ) ?
The graph of the function g(x) has an equation of g(x) = 6√(x - 3)
Identifying the graph of the function g(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = 3√x
The transformed function g(x) is given as
g(x) = 2f (x − 3)
In f(x) = 3√x , we have
f(x - 3) = 3√(x - 3)
Multiply both sides by 2
So, we have
2f(x - 3) = 2 * 3√(x - 3)
Evaluate the products
2f(x - 3) = 6√(x - 3)
Recall that
g(x) = 2f (x − 3)
So, we have
g(x) = 6√(x - 3)
This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)
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A biomedical manufacturing process has only 12.5% chance of producing a commercially successful result. The mean number of processes to be performed before a commercially successful one is?
The mean number of processes to be performed before a commercially successful one is 8.
The probability of success in each attempt is 0.125, so the parameter of the geometric distribution is p=0.125.
The mean of a geometric distribution with parameter p is equal to 1/p, so:
Mean = 1/p = 1/0.125 = 8
Therefore, the mean number of processes to be performed before a commercially successful one is 8.
In probability and statistics, the mean (or average) is a measure of the central tendency of a set of numbers. It is calculated by adding up all the numbers in a set and then dividing the sum by the total number of values in the set. The mean is a commonly used measure of the central tendency because it takes into account all the values in the set and provides a single value that represents the "typical" value.
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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle.
questions 1)
m
question 2)
m
question 3)
m
The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.
Option D is correct.
How to solveif angle A is obtuse and if a > b then the triangle has one solution
We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.
Finding remaining sides c and ∠B and ∠C
Using the Law of sines to find ∠B
a/sin A = b/sin B
7/sin 119° = 4/sin B
7 * sin B = 4 * sin 119
7*sin B = 4(0.874)
sin B = 3.496/7
B = sin^-1(0.4994)
B = 29.96 = 30°
We know that sum of angles of triangle = 180°
So, 180° = 119° + 30° +∠C
180° = 149° + ∠C
=> ∠C = 180° - 149°
∠C = 31°
Now finding c
b/sin B = c /sin C
4/Sin 30 = c/sin 31
4* sin 31 = c*sin 30
4*0.515 = c* 0.5
=> c = 4*0.515/0.5
c = 4.12 ≈ 4
So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.
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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree
A = 119°, a=7, b=4
Question 7 options:
one solution; c ≈ 7; B = 30°; C = 119°
no solution
one solution; c ≈ 4; B = 31°; C = 30°
one solution; c ≈ 4; B = 30°; C = 31°
pleaseeee help me!!
mathematics the pic below
Answer:
15, 18, 21, 24, 27, 30 ( +3)
7, 14, 28, 56, 112, 224, 448 ( x 2)
77, 70, 63, 56, 49, 42, 35 ( - 7)
20, 31, 42, 53, 64, 75, 86, 97 (+11)
22, 35, 48, 61, 74, 87 (+13)
PLS HELP ASAP
I AM SO CONFUSED WID THIS!
The numbers 1-20 are written on pieces of paper and put in a box. Two pieces of paper are randomly selected and not replaced.
a) Are the events dependent or independent? _________
b) What is the probability of selecting a number less than 6 both times? ________
the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.
how to find probability ?a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.
b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.
The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.
Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.
To find the probability of both events occurring, we multiply the probabilities:
P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)
P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19
Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.
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Express 1:0.2:0.75 in their simple form
Answer:
20 : 4 : 15
Step-by-step explanation:
1 : 0.2 : 0.75
1 : 2/10 : 75/100
1 : 20/100 : 75/100
(×100)
100 : 20 : 75
(÷5)
20 : 4 : 15
Given the following similar triangles, what is the area of triangle B?
A 1
B 1.8
C 3.2
D 5
The calculated area of the triangle B is 1.8 square units
What is the area of triangle BFrom the question, we have the following parameters that can be used in our computation:
Triangle A and B
Where
Area of A = 1/2 base * height
Sp, we have
Area of A = 1/2 * 2 * 5
Next, we have
Area of B = Area of A * Scale factor^2
Using the above as a guide, we have the following:
Area of B = 1/2 * 2 * 5 * (3/5)^2
Evaluate
Area of B = 1.8
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Anna wants to borrow $15,000 to buy a used sail boat. After looking at her financial situation, she realizes that she can only afford monthly payments of $300. The bank is offering financing at 6.1%. For how long will Anna need to finance the boat to stay within her monthly payment?
Answer:
47 months
Step-by-step explanation:
find 6.1% of 15k then divide that by 300
6.1% = 915
15,000 - 915 = 14085
14085 divided by 300 is 46.95 then rounded is 47
Which statement concerning the equation x² - 1 = x is true?
1. Its discriminant is 0, so it has no solution.
2. Its discriminant is 5, so it has two real solutions.
3. Its discriminant is 0, so it has one real solution.
4. Its discriminant is -3, so it has two complex solutions.
Answer:
The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = -1, and c = -1. So:
x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)
x = (1 ± sqrt(5)) / 2
Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.
whats the probility that she selects a non-mathamatical major, given that she choosees randomly from only sophmores From mrs. Burke's math class
The probability that Mrs. Burke selects a non-Mathematical major, given that she chooses randomly from only Sophomores is 51.5%.
What is the probability?Probability refers to the chance or likelihood of an event occurring given many possible events that could have occurred.
Probability is expressed as a quotient of the expected event or success and the total possible events, outcomes, or successes.
The number of Sophomores in Mathematics Majors = 16
The number of Sophomores in Non-Mathematics Majors = 17
The total number of Sophomores in Mrs. Burke's Mathematics Class = 33
The probability of selecting a non-Mathematical major, given that Mrs. Burke chooses randomly from only Sophomores = 51.5% (17 ÷ 33 x 100)
Mrs. Burke's Mathematics Class
Academic Year Mathematics Majors Non-Mathematics Majors Total
Freshmen 19 18 37
Sophomores 16 17 33
Juniors 11 15 26
Seniors 12 13 25
Total 58 63 121
Thus, the likelihood of choosing a non-Mathematical major from the Sophomores is 51.5%.
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Question Completion:Mrs. Burke's Mathematics Class
Academic Year Mathematics Majors Non-Mathematics Majors
Freshmen 19 18
Sophomores 16 17
Juniors 11 15
Seniors 12 13
The formula for the volume of a prism is V = area of base x height. What is the volume and surface area of each of these prisms? Show your thinking
The volume of the prism is V = 4000 cm³
Given data ,
Let the volume of the prism be represented as V
Now , the value of V is
Let the height of the prism be h = 10 cm
Let the width of the prism be w = 20 cm
Let the length of the prism be l = 20 cm
So , the base area of prism = l x w
Base area = 400 cm²
Now , the volume of the prism is V = 400 x 10
V = 4000 cm³
Hence , the volume of prism is V = 4000 cm³
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PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT
p = 3, q = 41, and r = 2, and we can write:
[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]
What is an arithmetic series?According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.
To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:
(141-5) = 22 + (n - 1)3
136 = 22 + 3n - 3
117 = 3n
n = 39
Therefore, there are 39 terms in the arithmetic series.
To find the sum of the first n terms of an arithmetic series, we can use the formula:
Sn = n/2(a1 + an)
where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:
S39 = 39/2(22 + (141-5))
S39 = 19(136)
S39 = 2584
Therefore, the sum of the first 39 terms of the series is 2584.
Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.
We know that the common difference is 3, so we can write the nth term as:
an = a1 + (n - 1)d
an = 22 + (n - 1)3
an = 3n + 19
Substituting this into the formula for the sum of the first n terms, we get:
Sn = n/2(a1 + an)
Sn = n/2(22 + 3n + 19)
Sn = n/2(3n + 41)
[tex]Sn = 3/2 n^2 + 41/2 n[/tex]
Therefore, p = 3, q = 41, and r = 2, and we can write:
[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]
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i need help as soon as possible!
Answer:
2600This is a probability conversion problem.
multiply 9/11 x 44/81
Answer:
Step-by-step explanation:
decimal: 0.44444444444
fraction: 4/9
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 15 square feet use 3.14 for pi
The distance from which the sprinkler can spread water is 4.37 feet
How to determine the valueTo determine the value, we need to know the area of the circle.
The formula for the area of a circle is expressed as;
A = πr²
Given that the parameters are;
A is the area of the circler is the radius of the circleSubstitute the values, we have;
15 = 3.14r²
Divide both sides by the coefficient, we get;
r² = 4. 77
find the square root of both sides, we get;
r = 2. 19 feet
But note that the formula for diameter is given as;
Diameter = 2radius
Diameter = 2(2.19)
multiply the values
Diameter = 4.37 feet
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The acts in a talent competition consist of 10 instrumentalists, 12 singers, and 8 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first?
Answer:
P=4/15
Step-by-step explanation:
P(dancer first) = 8/30=4/15
Which equation can be used to solve for x
Answer:
(a) 7(x +3.5x) = 56
Step-by-step explanation:
You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.
Daily runThe morning run is given as x.
The evening run is 3.5 times as long, so is 3.5x
The total mileage each day is (x +3.5x).
Weekly totalIn 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:
7(x +3.5x) = 56
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
7
7
22
The scale factor for this right triangles is equal to 5/4.
What is a scale factor?In Mathematics, the scale factor of any geometric figure can be determined by dividing the dimension or side length of the new figure (image) by the dimension or side length of the original figure (pre-image):
Scale factor = Dimension of new figure (image)/Dimension of original figure (pre-image)
By substituting the given dimensions into the formula for scale factor, we have;
Scale factor = image dimension/pre-image dimension
Scale factor = 15/12 = (25/4)/5
Scale factor = 5/4.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Anna saved $20 in a jar each month for 2 3/4 years. she spent 75% of her savings on a computer. how much money did anna have left in the jar
Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.
We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.
So, total months = 9 + 12 + 12 = 33
Now, using the multiplication operation, we get
⇒ Total money saved = 33 * 20
⇒ Total money saved = $660
It is given that she spent 75% of her savings on computer.
So, using the subtraction operation, we get
⇒ Amount left = 660 - 75%
⇒ Amount left = $165
Hence, Anna has $165 left in the jar.
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HELP THIS IS ALL!!!HELPPP
Answer:
247
Step-by-step explanation:
Use the estimated angle to find the distance of the life-raft from the lighthouse.
The correct angle of elevation for the lighthouse's top is roughly 1.91°.
How to find the distance of the lift-raft from the lighthouse?Consider the diagram drawn below, P is the position of the person in the lift-raft, B is the base of the lighthouse and the T is top of the lighthouse.
The diagram shows that the angle produced between the person in the life raft's line of sight to the top of the lighthouse and the horizontal is equal to the angle formed by the top of the lighthouse's height. Call this angle "[tex]\alpha[/tex]".
a) The distance "d" between the life raft and the lighthouse can be calculated using trigonometry.
[tex]tan\alpha = \frac{opposite}{adjacent} \\tan\alpha = \frac{20}{d}[/tex]
putting the value of [tex]\alpha[/tex] = 3 degrees put into the above equation.
[tex]tan3 = \frac{20}{d}[/tex]
[tex]d = \frac{20}{tan3}[/tex]
d = 354.14 (rounded to 2 decimal points
The life raft is therefore roughly 354.14 meters away from the lighthouse.
b)
Let's now calculate the proper angle of elevation for the situation when the life raft is 600 meters from the lighthouse.
[tex]tan\alpha = \frac{opposite}{adjacent}\\ tan\alpha = \frac{20}{600}[/tex]
solving for [tex]\alpha[/tex] we get,
[tex]\alpha = tan^{-1} (\frac{20}{100})\\\alpha = 1.91 degree\\[/tex]
Since the life raft is 600 meters from the lighthouse, the correct angle of elevation for the lighthouse's top is roughly 1.91°.
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The complete question in the form of the image below:
what are the answers to these questions?
a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.
b) The domain of V is [0, 3) in interval notation.
c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.
d) The maximum volume is 160/27 cm³.
(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.
Since the height of the box is x cm, the volume of the box can be expressed as
V = x(20-2x)(6-2x) cm³.
(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.
(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get
dV/dx = 4x³ - 52x² + 120x.
Setting dV/dx = 0, we get
x = 0 or x = 3 or x = 10/3.
Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.
We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get
V(0) = V(3) = 0
and
V(10/3) = 160/27.
(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.
So, the length of the box is
20-2(10/3)
= 40/3 cm,
the width of the box is
6-2(10/3)
= 2/3 cm, and
the height of the box is 10/3 cm.
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Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5
z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2
PLease help
the perimeter of a triangle is 53 inches. the length of the one side is 15 inches the other two sides are congruent find the lengths
Average Weekly Earnings in Canada
Occupation 2010 2008
Forestry, logging and support $971 $812
Manufacturing $977 $943
Transportation and warehousing $900 $873
Construction $1071 $1023
Retail trade $501 $486
1. Calculate the mean (average) weekly earnings of workers in the occupations
listed for 2010.
Answer: To calculate the mean weekly earnings for each occupation in 2010, we need to add up the weekly earnings for each occupation and divide by the number of occupations.
For Forestry, logging and support:
Mean weekly earnings = (971) / (1) = $971
For Manufacturing:
Mean weekly earnings = (977) / (1) = $977
For Transportation and warehousing:
Mean weekly earnings = (900) / (1) = $900
For Construction:
Mean weekly earnings = (1071) / (1) = $1071
For Retail trade:
Mean weekly earnings = (501) / (1) = $501
Therefore, the mean weekly earnings for workers in the listed occupations in 2010 are:
Forestry, logging and support: $971
Manufacturing: $977
Transportation and warehousing: $900
Construction: $1071
Retail trade: $501
Step-by-step explanation: