Probability of an event = (number of favorable event) / (total number of event).
P(B) = (Event B) / (total number of event).
Probability of getting 1 = 1/6.
Rolling dice is an independent event, it is not dependent on how many times it’s been rolled.
Probability of getting 1 three times in a row = probability of getting 1 first time × probability of getting 1 second time × probability of getting 1 third time.
Probability of getting 1 three times in a row = (1/6) × (1/6) × (1/6) = 1/216.
Hence, the probability of getting 1 three times in a row is 0.463%.
13. Communicate and Justify A sequence starts with 16. The pattern is divide by 2. Another sequence starts with 1. The pattern is multiply by 2. Do the two sequences have the same number in the same position? Explain.
The two sequences have the same number (4) in the same position (third)
How to determine if the two sequences have the same number in the same position?From the question, we have the following parameters that can be used in our computation:
A sequence starts with 16. The pattern is divide by 2. Another sequence starts with 1. The pattern is multiply by 2Using the above as a guide, we have
Sequence 1: 16, 8, 4, 2, 1.....
Sequence 2: 1, 2, 4, 8, 16.....
The number 4 is in the same position for the two sequences
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Which of the following statements is true?
For a large enough sample size, the Central Limit Theorem states that the sample medians of repeated samples of a population are normally distributed.
For the Central Limit Theorem to be true, you must have a large sample, the underlying population must be normally distributed, and the standard deviation should not be finite.
For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed.
Even with a very large sample size, the Central Limit Theorem states that the sample means of repeated samples of a population cannot be normally distributed.
The option that is true for the central limit theorem is;
C: For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed
Let us look at all the given options to access which one clearly is correct about the central limit theorem;
a) This option is incorrect because the CLT theorem is based on ‘sample mean’ distribution.
b) This option is Incorrect because the theorem is true for any population distribution.
c) This option is correct because Irrespective of the population distribution, the sample means of repeated samples are normally distributed for larger n.
d) The “central limit theorem(CLT)” states that, the sample means of the repeated samples follows normal distribution for ‘large’ sample sizes. Thus, this option is incorrect.
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Given parallelogram abcd, in order to prove that opposite sides are congruent, what additional segments or points will you need?.
Answer:
Step-by-step explanation:
In a parallelogram, opposite sides are congruent. To prove this, you would need to show that the following two conditions are true:
The length of one pair of opposite sides is equal.
The two pairs of opposite sides are parallel.
To show these two conditions, you may need additional segments or points such as:
Perpendicular lines or segments to the sides to help show the sides are parallel.
Diagonal segments to help show that the parallelogram is a rectangle and that the sides are equal in length.
By showing these two conditions, you can conclude that the opposite sides of a parallelogram are congruent.
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as a principal amount with an interest of 3% compounded quarterly Brooklyn
wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly Explain which method results in more money after 2 years Show all work
Answer:
To compare the amount of money that Patrick and Brooklyn would have after 2 years, we need to calculate the interest earned using each of their methods.
For Patrick, who deposited $300 with an interest rate of 3% compounded quarterly, the formula to calculate the amount after 2 years (8 quarters) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (3%)
n = number of times compounded per year (4)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.03/4)^(4 * 2)
A = $300(1.0075)^8
A = $300 * 1.06173
A = $318.52
For Brooklyn, who deposited $300 with an interest rate of 5% compounded monthly, the formula to calculate the amount after 2 years (24 months) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (5%)
n = number of times compounded per year (12)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.05/12)^(12 * 2)
A = $300(1.00417)^24
A = $300 * 1.09722
A = $328.17
Therefore, after 2 years, Brooklyn would have $328.17, which is more money than Patrick's $318.52.
please and answers please just need help
Answer:
100π - 192 or 122.159....
Step-by-step explanation:
In order to find the diameter we much first split the rectangle diagonally and find the hypotenuse using Pythagorean theorem.
a^2 + b^2 = c^2
16^2 + 12^2 = c^2
400 = c^2
c = 20
If the diameter of the rectangle is 20, the radius is just half of that which is 10. Then you just need to a do a basic calculation for area of a circle and then subtract out the area of the rectangle.
Area of circle = πr^2 = π(10^2) = 100π (keeping it in exact value since π is infinite)
Area of rectangle = lw = (16)(12) = 192
Area of shaded area = 100π - 192 (exact) = 122.159 (estimate)
A train travelling at 105km/hr goes through a tunnel 1575m long. Calculate in seconds,the time a passenger on the train spends in the tunnel
Correct me if im wrong :)
What is the equation of the midline for the function given? f(x) = 9sin3x + -5.
After answering the provided question, we can say that the function's midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5
What exactly is an equation?A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2. midpoint equation = 9sin3x + -5 => f(1) = 9*0 + 5 = 5
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Solve the system by substitution.
y = 5x
y = 4x + 9
Answer:
x=9
Step-by-step explanation:
Since y=5x, you plug it into the other equation's y and it'd look like this 5x=4x+9. Then you subtract 4x on both sides and that would leave you with an x=9.
Use the discriminant to describe the solutions as one real, two real, or two
imaginary solutions.
4. x2 − 15x + 12 = 0 5. 3x2 − 6x + 4 = 0
The Equation x² − 15x + 12 = 0 have two Real solution and 3x² − 6x + 4 = 0 have Imaginary solution.
What is solution to the Equation?The discriminant, denoted by the equation b² - 4ac, can be used to ascertain if the solutions are real, repetitive, or complex:
1) If the discriminant is smaller than 0, there are two imaginary roots to the problem (s).
2) The equation has one repeating real solution if the discriminant equals zero (s).
Given:
x² − 15x + 12 = 0
Solving the Quadratic Equation
x² − 15x + 12 = 0
D = b² - 4ac
D = (-15)² - 4(1)(12)
D = 225 - 48
D = 177 >0
So, the Equation will have two Real solution.
b) 3x² − 6x + 4 = 0
Solving the Quadratic Equation
3x² − 6x + 4 = 0
D = b² - 4ac
D = (-6)² - 4(3)(4)
D = 36 - 48
D = -12 >0
So, the Equation will have Imaginary solution.
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Need help quick with this problem!!!!
The product of a, b, and c is 27/8.
What is an expression?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, and parentheses) that represents a quantity or a mathematical relationship. Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved.
The given expression is
[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2} }[/tex]
To simplify the given expression and write it in the form of ax^by^c, we can start by using the properties of exponents and simplifying the numerator and denominator separately:
Numerator: [tex]6x^2y^(-1) = \frac{6x^2}{y}[/tex]
Denominator: [tex]\sqrt[4]{(16x^5y^2)} = (16x^5y^2)^{(1/4)} = 2x^{(5/4)}y^{(1/2)}[/tex]
Putting the simplified numerator and denominator together, we have:
[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2}} = \frac{6x^2}{y} \cdot \frac{1}{2x^{5/4}y^{1/2}} = \frac{3}{\sqrt{2} \cdot x^{3/4}y^{3/2}}[/tex]
Now we can see that the given expression can be written in the form of ax^by^c, where a = 3, b = -3/4, and c = -3/2. Therefore, the product of a, b, and c is:
a * b * c = 3 * (-3/4) * (-3/2) = 27/8.
Hence, the product of a, b, and c is 27/8.
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A container of gas at 29 psi is compressed to
one seventh its original volume. What is the
new pressure of the gas?
Answer in units of psi
Step-by-step explanation:
Since the original volume is 29 and they are looking for 1/7th of that, we can multiply these two numbers
[tex](29)( \frac{1}{7} ) = 4 \frac{1}{7} psi[/tex]
Tuna can be bought in 12-oz cans for $1.10 each or in 10 oz cans that sell for $0.98 each. Which is a better buy? USE UNIT RATIOS TO ANSWER THIS PROBLEM.
Answer: Option 1
Step-by-step explanation:
I'd say the easiest way would be to find the prize per oz in both options
Option 1: $1.10/12oz = approx 0.092 (so around 9 pennies)
Option 2: $0.98/10oz = 0.098 (also 9 pennies but still slightly more than option 1)
You can check by choosing a random number of oz and multiplying them by the price to see which costs more
ex: 120 oz
option 1 : 10 x 1.10 = $11
option 2: 12 x 0.98 = $11.76
2. Evelyn creates a one sample z interval for proportions and gets a margin of error of 0.0758. If her sample
proportion was 0.75 and her sample size was 100, what level of confidence did she use?
a. 90%
b. 92%
c. 94%
d. 96%
e. 98%
The level of confidence Evelyn used is 92%. Therefore, option B is the correct answer.
What is a confidence interval?The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
Given that, one sample z interval for proportions and gets a margin of error of 0.0758.
If her sample proportion was 0.75 and her sample size was 100.
We know that, p±z×√p(1-p)/n
Where, P is sample proportion, n is the sample size and z is the standardized normal distribution
Here, 0.75±0.0758×√0.75(1-0.75)/100
= 0.75±0.0758×√0.1875/100
= 0.92
=92%
Therefore, option B is the correct answer.
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Aubrey broke a cell sample into 15 batches, each way 1.3×10 to the -7th grams. How much did the original sample weigh? Use scientific notation to express your answer.
Answer:
Step-by-step explanation:
1.3 * 10 ^-7
is 0.00000013
0.00000013 times 15 is
0.00000195.
0.00000195 in scientific notation is
1.95*10^-6
Which of the symbols correctly relates the two numbers below? Check all that
apply.
A. =
B. >
C. Z
☐ D. <
E. >
OF. s
364? 225
The symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
The solution has been obtained by using concept of relational symbols.
What are relational symbols?
Relational symbols are used in mathematics to represent mathematical relations, which combine with one or more other mathematical objects to construct complete mathematical statements. These are the relational symbols for equality and comparison in arithmetic and common mathematics.
We are given 2 numbers as 364 and 225.
It is clearly visible that both the numbers are not same so, the symbol '≠' depicts the relationship between the two numbers.
Also, we know that the number 364 is greater than 225. So the another symbol depicting relation between the numbers is '>'.
Hence, the symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
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Question: Which of the symbols correctly relates the two numbers below? Check all that apply.
364? 225
A. =
B. >
C. ≥
D. <
E. ≤
F. ≠
Need help with this question pls?
The given amounts of money will be written as £5.37, £2.04 and £15.70 respectively. The solution has been obtained by using denominations of money.
What is denomination?
The term "denomination" refers to the units of measure that are used to categorize various financial products such as coins and paper money. Every country has different denomination.
We are given three different amounts of money in words which are to be written in denominations.
So,
a. Five pounds and thirty seven pence = £5.37
b. Two pounds and four pence = £2.04
c. Fifteen pounds and seventy pence = £15.70
Hence, the amounts in their denominations have been obtained.
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The sum of two numbers is 160. One number is 40 more than the other. Find the numbers.
The larger number is
The smaller number is
Answer:
The larger number is 100
The smaller number is 60
Step-by-step explanation:
x + (40 + x) = 160
2x + 40 = 160
x + 20 = 80
x = 60
60 + (40 + 60) = 160
160 = 160
Help!! Geometry:((!!!!
Answer:
x=2
y=0
Step-by-step explanation:
2x=4
x=4/2
x=2
again,
y-1 =2y -1
1-1 =2y -y
0=y
All of the following constructions start with a line segment except...
O constructing a 45° angle
O constructing a 30° angle
O constructing congruent angles
• constructing equilateral triangles
All of the aforementioned structures, with the exception of creating equilateral triangles, begin with a line segment.
What is meant by line segment?The component of a line in a geometric shape, such as a triangle, circle, quadrilateral, etc., that is bordered by two (2) distinct points and usually has a definite length is referred to as a line segment.
An equilateral triangle is a particular kind of triangle with equal side lengths and identical angles at each of its three (3) internal sides.
A line segment serves as the foundation for the following angles and lines in geometry:
The process of creating a line perpendicular to a point on a line.
The creation of a 45-degree angle (45°).
The creation of a 30-degree (30-degree) angle.
Since an equilateral triangle has equal side lengths and all three of its interior angles are equal, we can reasonably and logically conclude that its construction does not begin with a line segment.
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how to solve equation below
Answer: (a) -6x²y
Step-by-step explanation:
[tex]\frac{-18x^{3}y^{2} }{3x^{2} y}[/tex]
X to the power of 2 should be cancelled from the top and bottom, which leads to:
[tex]\frac{-18xy^{2} }{3y}[/tex]
Then Y to the power of 1 should be cancelled from top and bottom (since it can go into both), which leads to:
[tex]\frac{-18xy}{3}[/tex]
Then find the highest common factor (which is 3), and cancel it out from the top and bottom, which leads to:
[tex]\frac{-6xy}{1}[/tex]
which equals to
-6x²y (a)
The population of two different villages is modeled by the equations shown. Suppose y represents the population and x represents the number of years since 1980. What year(s) were the populations of both villages the same? What was the population of both villages in the year(s) they were the same?
Step-by-step explanation:
Hope it helps :) #CarryOnLearning
convert 31,750 feet into miles
To convert 31,750 feet to miles, divide the number of feet by the number of feet per mile:
31,750 feet / 5,280 feet/mile = 6 miles
Find the slope of a line parallel to 25x-5y=-10
.
The slope of a line parallel to another line will have the same slope as the original line. To find the slope of the line 25x - 5y = -10, we need to rearrange the equation into the slope-intercept form y = mx + b, where m is the slope.
First, we'll isolate y:
25x - 5y = -10
5y = 25x + 10
y = (25/5)x + 2
So the slope of the line 25x - 5y = -10 is m = 25/5 = 5.
Therefore, a line parallel to 25x - 5y = -10 will have a slope of m = 5.
210 people are asked how many siblings they have?
# of Siblings Frequency Relative Frequency Cumulative Frequency
43
43
41
0
1
2
3
4
43
Submit Question
0.2048
0.2048
0.2048
0.1905
43
86
127
210
a. Complete the table (Use 4 decimal places when applicable)
b. What percent of the people have exactly one sibling?
Hint: Frequency Tables
The frequency table is completed and the percent of the people who have exactly one sibling is 20.48%.
What is Relative Frequency and Cumulative Frequency?Relative frequency is found by dividing the frequency with the total number of values.
Cumulative frequency is calculated by adding the previous frequencies together.
(a) From the table,
Total number of people = 210
So, Total frequency = 210
Frequency of number of siblings as 4 = 210 - (43 + 43 + 41 + 43) = 40
Relative frequency = Frequency / Total frequency
Relative frequency of number of siblings as 2 = 0.1952
Cumulative frequency of number of siblings as 3 = 127 + 43 = 170
(b) Percent of people having exactly 1 sibling = (43 / 210) × 100
= 20.48%
Hence the percent of people having exactly 1 sibling is 20.48%.
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A graphing calculator is recommended. In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in, by 20 in. by cutting out equal squares of side x at eech corner and then folding up the sides (see the figure). 20 in. 12 in. (a) Find a function that models the volume V of the box. (b) Find the values of x for which the volume is greater than 230 in2. (Rgund your answers to three decimal places. Enter your answer using interval notation) (c) Find the largest volume that such a box can have. (Round your answer to three decimal places) in2
A function modeling the volume of the box can be found, and the values of x for which the volume is greater than 230 in2 are x = [-2.636, 2.636]. The largest volume is 480 in2, which is achieved when x = 5.
A function that models the volume V of the box can be found by subtracting four [tex]x2[/tex]from both the length and the width, and then multiplying the result to get the volume:
V = [tex](12 - 4x2)(20 - 4x2)[/tex]
To find the values of x for which the volume is greater than 230 in2, we can solve the equation
V = [tex](12 - 4x2)(20 - 4x2) = 230[/tex] for x.
This gives x values of ±2.636
Thus, the values of x for which the volume is greater than 230 in2 are x = [[tex]-2.636, 2.636[/tex]].
The largest volume that such a box can have is 480 in2, which is obtained when x is equal to the length or width divided by two. This occurs when x = 10/2 = 5. Thus, the largest volume that such a box can have is 480 in2.
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Name
2-Step Word Problems
There were 24 polar bears and 38
penguins swimming in the ocean. 15
polar bears got out of the water.
How many polar bears and penguins
are left playing in the water?
polar bears and penguins
My brother made 46 snowballs and I
made 59 snowballs. My sister joined
us and made 25 more snowballs.
How many snowballs do we have
altogether?
i
My mother had a collection of 51
snow globes. She received 8 more
snow globes for her birthday. My
brother and I started fighting and
broke 12 snow globes. How many
snow globes does my mother have
left?
snowballs
snow globes
-
ate:
There were 83 adult penguins and
69 baby penguins playing on the hill.
55 mother penguins went home.
How many penguins are left playing
on the hill?
penguinsi
There are 47 polar bears and penguins in the water.
The number of snowballs made altogether is 130 snowballs.
The number of snow globes your mother has left is 47 snow globes.
The number of penguins left playing is 97 penguins.
How to solve word problems?Number of polar bears= 24
Number of penguins = 38
No. of polar bears that got out of the water= 15
Total polar bears and penguins in the water = (24 + 38) - 15
= 47
Number of snowballs made by your brother = 46
Number of snowballs made by you = 59
Number of snowballs made by your sister, brother and you = 25
Total snowballs made= 46 + 59 + 25
= 130 snowballs
Number of snow globes mother has = 51
Number of additional snow globes received = 8
Number of snow globes broken = 12
The number of snow globes your mother has left= (51 + 8) - 12
= 59 - 12
= 47 snow globes
Number of adult penguins(mother and father) = 83
Number of baby penguins = 69
Number of mother penguins that went home = 55
Number of penguins left playing = (83 + 69) - 55
= 97 penguins.
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Find the power of 9↑1. Type your answer using digits.
Answer:
9^1 has a power of 1. it evaluates to 9
Step-by-step explanation:
Using logarithmic properties, what is the solution to log4(y - 9) + log43 = log481? Show all necessary steps.
Answer:
y = 36
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_4(y-9)+\log_43=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log product law}}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_4\left(3(y-9)\right)=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log equality law}}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]
[tex]\implies 3(y-9)=81[/tex]
Divide both sides of the equation by 3:
[tex]\implies \dfrac{3(y-9)}{3}=\dfrac{81}{3}[/tex]
[tex]\implies y-9=27[/tex]
Add 9 to both sides of the equation:
[tex]\implies y-9+9=27+9[/tex]
[tex]\implies y=36[/tex]
Therefore, the solution to the given logarithmic equation is y = 36.
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75. What equation can you write to solve for x
The solution is, the value is, x = 49.6.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
given that,
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75
so, 1 + 2 = 180
or, 106 + 3x - 75 = 180
or, 3x = 149
or, x = 49.6
Hence, The solution is, the value is, x = 49.6.
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Help!!!!
I am very lost!
The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.
How to find the height of the plane?A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .
Therefore, the height of the plane can be found as follows:
The situation forms a right angle triangle.
Using trigonometric ratios,
tan 12 = opposite / adjacent
tan 12° = x / 4812
cross multiply
x = 4812 tan 12°
x = 4812 × 0.21255656167
Therefore,
x = 1022.82217476
x = 1023 metres.
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