The probability that a student studied for exactly 1 hour is 0.23
How to determine the probability that a student studied for exactly 1 hour?Probability is a measure of the likelihood of a particular event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
From the given table, you need notice that the number of students who study for 1 hour is 8.
In order to determine the probability that a student studied for exactly 1 hour, we need to find total number of students. That is:
Total number of student = 1 + 8 + 2 + 5 + 9 + 7 + 3 = 35
probability (exactly 1 hour) = number of exactly 1 hour/Total number
probability (exactly 1 hour) = 8/35 = 0.23
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Answer:
B
Step-by-step explanation:
a study was conducted to help determine which of the top two political parties the general population would prefer to vote for in the up-coming election. in determining whom to include in the sample, two stages were involved. at the first stage, a random sample of 50 individuals was selected from each of the 20 regions in the country and then pooled into a combined sample of 1,000. at the second stage, these 1,000 individuals were divided into 5 income-level groups, and a random sample of 50 from each group was selected. Select all of the statements regarding the sampling design in the above scenario that are true:
The study does not involve a voluntary response.
The first stage creates a stratified random sample.
The whole study creates a multistage random sample.
The second stage involves simple random sampling only.
The true statements are the study does not involve a voluntary response, the first stage creates a stratified random sample and the whole study creates a multistage random sample.
In the given question, the study done ideally creates a multistage random sample. There are two parts to the sampling process for the study in the given question. Initially, a combined sample of thousand of individuals was assembled by combining a randomly selected sample of fifty individuals, that were from each of the 20 regions of each nation. The next step was to choose a random sample of fifty individuals from every one of the five income groups represented among those 1,000 individuals.
Additionally, because the study doesn't entirely rely on a discretionary answer, individuals were picked by a random sample approach rather than explicitly or through self-selection. A stratified random sample is also created during the initial step. This shows that a random sample was drawn from each subgroup after the dataset was separated into groups.
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Answer both part a and b the problem
a. Equation for Bert to figure out Ernie's original number is x = 5(2x - 6) + (-6).
b. Ernie's original number/integer was 4.
c. On checking and verifying the original integer is obtained as 4.
What is integers?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Ernie picks an integer from 1 to 10.
Let the value of the integer be x.
First the number is doubled, so the value of integer becomes = 2x.
Then 6 is subtracted from the number, so the value of integer becomes = 2x - 6.
Then the entire difference is multiplied by 5, so the value of integer becomes = 5(2x - 6).
Lastly -6 is added to the product, so the value of integer becomes = 5(2x - 6) + (-6).
So, the equation to find the integer is -
x = 5(2x - 6) + (-6)
Now, simplify this expression to obtain the number.
x = 5(2x - 6) + (-6)
x = 10x - 30 - 6
x - 10x = -36
-9x = -36
x = -36/-9
x = 4
Check if 4 is the correct number -
First the number is doubled = 4 × 2 = 8
Subtract 6 from the number = 8 - 6 = 2
Then multiply the difference by 5 = 5 × 2 = 10
Then subtract -6 from the number = 10 - 6 = 4
Therefore, the original number was 4.
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From 1994 to 2003, the amount of athletic equipment E (in millions of dollars) sold domestically can be modeled by E(t) = -10t^3 + 140t^2 - 20t + 18,150where t is the number of years since 1994. Use the following steps to find the year when about $20,300,000,000 of athletic equipment was sold. a. Write a polynomial equation that can be used to find the answer. b. List the possible whole-number solutions of the equation in part (a) that are less than 10.c. Use synthetic division to determine which of the possible solutions in part (b) is an actual solution. Then calculate the year which corresponds to the solution.
In a synthetic polynomial , the real solution of 2 is found; the year is 1996, and $20,300,000,000 was sold.
a. 20,300,000,000 = -10t^3 + 140t^2 - 20t + 18,150
b. Suggestions for the problem: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
b. To solve, use synthetic division; the solution is 2; the year is 1996.
In order to discover the year in which the specified quantity of sporting equipment was sold, we must create a polynomial equation. E(t) = -10t3 + 140t2 - 20t + 18,150, where t is the number of years since 1994, is the equation given in the problem. We must rewrite the equation so that the right side equals 20,300,000,000 in order to determine the year in which $20,300,000,000 worth of sporting equipment was sold. After that, the equation is 20,300,000,000 = -10t3 + 140t2 - 20t + 18,150, which needs to be solved. The equation can have whole-number solutions that are less than 10, including 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We may use synthetic division to identify which of these answers is the true solution. this method, the coefficients of the equation are divided by the coefficient of the equation with the highest degree, and the quotient is then multiplied by the solution. Until the last portion is identified, this process is repeated. The answer is the quantity that equals the remainder.
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Based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). Which of the following statements is true?
answer choices
90% of the time, the mean amount of money that all students spend on lunch at this high school will be between $3.45 and $4.15.
90% of all students spend between $3.45 and $4.15 on lunch at this high school.
90% of all random samples of 50 students obtained at this high school would result in a sample mean amount of money students spend on lunch between $3.45 and $4.15.
90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.
Approximately 45 of the 50 students in the random sample will spend between $3.45 and $4.15 on lunch at this high school.
The right answer is that a 90% confidence interval containing the actual mean amount of money kids spend on lunch would be produced by 90% of all random samples of 50 students collected at this high school.
It is given that the 90% confidence interval for the mean amount of money students spend on lunch time at a high school is ($3.45,$4.15)
A 90% confidence interval interprets that, 90% of the random samples will result in a 90% confidence interval that contain the true value of the population parameter.
In other words, 90% of the random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.
Thus, the correct answer is option (D) or The right answer is that a 90% confidence interval containing the actual mean amount of money kids spend on lunch would be produced by 90% of all random samples of 50 students collected at this high school.
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The area of a square with a side 2.4m in length
Answer:
Below
Step-by-step explanation:
Squares have equal side lengths
area = side X side
= 2.4 m X 2.4 M = 5.76 m^2
the expression \root(4)(10mn) and (10mn)^((1)/(4))are equivalent or not equivalent
The expression \root(4)(10mn) and (10mn)^((1)/(4)) are equivalent
What are index forms?Index forms are described as that number written in the form of an exponential expression.
It is also described as a single number raised to another number.
The exponent of an exponential expression explains how many times to multiply the base by itself to simply the expression.
Standard forms and scientific notation are other names for index forms.
It is important to note that the fourth root of a number or variable is the biquadratic root.
From the information given, we have that;
[tex]\sqrt[4]{10mn}[/tex]
[tex](10mn)^1^/^4[/tex]
Note the following;
√2 = 2^1/2
∛2 = 2^1/3
Hence, the expressions are equivalent
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Find the 45th term of the arithmetic sequence an = 2 + 4(n − 1).
Group of answer choices
182
178
145
264
Step-by-Step Explanation:
n = 45
Therefore, 2 + 4(n - 1)
Putting n = 45, we have
2 + 4(45 - 1)
= 2 + 4 × 44
= 2 + 176
= 178
Answer:
B) 178
Hope it helps.
If you have any query, feel free to ask.
Sandra wants to buy an Apple iPad Pro (12.9-inch display) costing $900.00. Her parents have agreed to pay $5 for every $2 that Sandra saves. How much will each contribute?
To purchase the Apple iPad Pro, based on an equation, Sandra contributed $257 while her parents contributed $643.
What is an equation?An equation is a mathematical statement that states that two or more mathematical expressions are equal or equivalent.
Mathematical expressions are depicted as equations using variables, constants, numbers, and values and the equation symbol (=).
The total cost of the Apple iPad Pro = $900
The contribution of Sandra's parents per $2 = $5
The contribution of Sandra = $2
Let x = the variable contributed by each party
Equations:2x + 5x = 900
7x = 900
x = 128.57
Sandra's contribution = $257 (2 x 128.57)
Parents contribution = $643 (5 x 128.57)
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Lena is on a two week bicycle trip. After 5 days she had ridden 212 miles. Express Lena’s rate as a unit rate.
The unit rate of Lena's bicycle trip if she travelled 212 miles in 5 days is 42.4 miles per day
What is Lena's unit rate?Unit rate refers to the rate of traveling in miles per day.
Number of miles Lena has ridden= 212 miles
Number of days = 5 days
Lena’s rate as a unit rate = Number of miles Lena has ridden / Number of days
= 212 miles / 5 days
= 42.4 miles per day
Hence, Lena is traveling at a unit rate of 42.4 miles per day.
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A two member beach volleyball team decided they wanted new uniforms. The
swimsuits cost $58 and the visors cost $24 each. What is the total cost of the new
uniform for all of the members?
O $58
O $82
O $116
O $164
Calculate the volume of the Surface Area of pyramid 12cm height and 12cm base and 14cm weights
The volume of the pyramid is, 72 cm³.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Height of pyramid = 12 cm
Base of pyramid = 12 cm
Weight of pyramid = 14 cm
Now, We know that;
⇒ Volume of pyramid = 1/2 × Base × Height
Substitute all the values, we get;
⇒ Volume of pyramid = 1/2 × 12 × 12
⇒ Volume of pyramid = 6 × 12
⇒ Volume of pyramid = 72 cm³
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A 12-foot ladder is leaned against the side of a building. If the bottom of the ladder
rests 3 feet from the wall, determine the height at which the top of the ladder rests
on the wall. Let h represent the height. Show all the steps. Don’t forget the units!!!
Draw the diagram and label it. Solve:
Therefore statement:
Answer:
11.6 ft
Step-by-step explanation:
|\
| \
| \
| \
h | \ 12 ft
| \
| \
| \
| \
------------------------
3 ft
Use the Pythagorean theorem: a² + b² = c²
(3 ft)² + h² = (12 ft)²
9 ft² + h² = 144 ft²
h² = 135 ft²
h = √(135 ft²)
h = 11.6 ft
find the maclauvins series of f(x) = x ln(2x+1) what in the rc of the obtained seties
The Maclaurin series is xln(2x + 1) - x^2 + (2x^3)/3 - (2x^4)/4 + ... and the arc is (-1/2, 1/2).
How to determine the Maclaurin seriesFrom the question, we have the following parameters that can be used in our computation:
f(x) = x ln(2x+1)
The Maclaurin series of f(x) = x ln(2x + 1) can be found by using the power series expansion of the logarithm function and the definition of a derivative.
Starting with the power series expansion of ln(1 + x):
ln(1 + x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...
We can then substitute x = 2x + 1 - 1 to obtain the power series expansion of ln(2x + 1):
ln(2x + 1) = (2x + 1 - 1) - (2x + 1 - 1)^2/2 + (2x + 1 - 1)^3/3 - (2x + 1 - 1)^4/4 + ...
= 2x - x^2 + (2x^3)/3 - (2x^4)/4 + ...
Next, we use the definition of a derivative to find the Maclaurin series of f(x) = x ln(2x + 1):
f'(x) = d/dx (x ln(2x + 1)) = ln(2x + 1) + x * d/dx ln(2x + 1)
= ln(2x + 1) + x * (2 - 2x + 2x^2 - 2x^3 + ...)
= ln(2x + 1) + 2x - 2x^2 + 2x^3 - 2x^4 + ...
Therefore, the Maclaurin series of f(x) = x ln(2x + 1) is:
f(x) = ∫ f'(x) dx = ∫ (ln(2x + 1) + 2x - 2x^2 + 2x^3 - 2x^4 + ...) dx
= xln(2x + 1) - x^2 + (2x^3)/3 - (2x^4)/4 + ...
How to determine the arc of the seriesThe arc of a Maclaurin series refers to the range of values for x for which the series converges to the actual value of the function.
For the Maclaurin series above, the range of convergence depends on the function ln(2x + 1) which has a singularity at x = -1/2.
This implies that the Maclaurin series converges for all x such that |x| < 1/2.
Rewrite as
(-1/2, 1/2)
So, the arc of the series is (-1/2, 1/2).
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Harry places a ladder against his house to fix the roof, leaving 5 feet between the edge of the house and the ladder. The roof is 18 feet off the ground. Using the Triangle Inequality Theorem, determine the range of heights his ladder should have.
Using the Triangle Inequality Theorem, the range of heights his ladder should have would be greater than or = 23 feet.
What is Triangle Inequality Theorem?The Triangle Inequality Theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
That is c >/= a + b
a = 5 feet
b = 18 feet
C >/ = 5+18 = 23 feet
Therefore, the range of heights his ladder should have would be greater than or = 23 feet.
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In the cuboid below all lengths are in centimetres. The cuboid has a volume of 196cm cubed. Find the value of k.
The value of k in the cuboid is 7 cm when the volume is 196cm³.
What is volume?The space taken up by any three-dimensional solid constitutes a volume, to put it simply. They can be a cube, cuboid, cone, cylinder, or sphere.
The volumes of various shapes vary. In three-dimensional geometry, we have examined a variety of solids and shapes that are defined in three dimensions, including cubes, cuboids, cylinders, cones, etc. We are going to learn to calculate the volume for each of these shapes.
The volume of cuboid = l × b × h
Here,
4 × k × k = 196cm³
k² = 196/4
k² = 49
k = √49
k = 7
Thus, The value of k in the cuboid is 7 cm when the volume is 196cm³.
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Andy buys x cakes.
Betty buy 4 times as much as Andy
Colin buy 3 times as much as Betty
Each cake costs 65p
The total cost was £52.65
How much cakes did each person buy?
Each person buys a number of cakes
Andy: 13Betty: 52Colin:16What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy
So,
Andy has = x Cakes
Betty have = 4x Cakes
Clin has = x +3 Cakes
Since each cake costs 65p and the total cost of the cakes is £52.65
thus,
0.65( x + 4x + x +3) = 52.62
x + 4x + x +3 = 81
6x = 78
x = 13
Therefore,
Andy has = 13 cakes
Betty has = 4x = 4*13 = 52 cakes
Colin has = x + 3 = 16 cakes
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Identify the type of sampling used in this example.
A researcher randomly selected 50 of the nation's middle schools and interviewed all of the teachers at each school. a. random
b. cluster
c. stratified
d. systematic
The type of sampling used in this example is a. random sampling
One of the most straightforward methods for gathering information from the entire population is random sampling. Every member of the subset has an equal chance of being chosen as part of the sampling process when using random sampling. For instance, if an organization employs 300 people overall, a sample group of 30 workers will be chosen to participate in the survey. In this instance, the population is the entire workforce of the organization, and the sample is 30 employees. Since all of the employees who were picked to participate in the survey were chosen at random, every worker has an equal chance of getting chosen.
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Many people say they want to be rich. What are some legitimate ways you can become financially wealthy as an adult? Your own words!
Answer:
see below
Step-by-step explanation:
1. study hard and go to a good college and then find a good job.
2. be intelligent on spending and save money to invest in the financial markets
3. buy a few life insurance policies with living benefits.
4. find a niche on social media and create contents to attract followers, and then invest the earnings in stock market or bond market.
5. invest in real estate
6. start a small business and then grow into franchise.
Write an explicit formula for a(n), the n(th) term of the sequence 11,4,-3, ....
The explicit formula that represents the nth term of the sequence will be aₙ = 18 - 7n.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The arithmetic sequence is given below.
11, 4, -3, .....
The first term is 11. And the common difference is given as,
d = 4 - 11
d = - 7
The explicit formula that represents the nth term of the sequence is given as,
aₙ = a₁ + (n - 1)d
aₙ = 11 + (n - 1)(-7)
aₙ = 11 - 7n + 7
aₙ = 18 - 7n
The explicit formula that represents the nth term of the sequence will be aₙ = 18 - 7n.
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Find the Unknown value of the triangle: Trigonometry
The unknown values in the triangle is calculated to be
PL = 14.3 cm
CY = 7.74
NY = 9.9 mm
LJ = 8.3
How to find the unknown values in the triangleThe unknown values in the triangle is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
1. using Sin = opposite / hypotenuse - SOH
sin x = PL / PX
sin 54.25 = PL / 17.62
PL = sin 54.25 * 17.62
PL = 14.3 cm
2. using Tan = opposite / adjacent - TOA
tan 52.67 = CY / 5.9
tan 52.67 * 5.9 = CY
CY = 7.74
3. using Sin = opposite / hypotenuse - SOH
sin 33.06 = YC / NY
NY = 5.4 / sin 33.06
NY = 9.9 mm
4. using Tan = opposite / adjacent - TOA
tan 55.05 = LJ / VJ
tan 55.05 * 5.8 = LJ
LJ = 8.3
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C Question 2 (SO3, AC1, AC2, AC3, AC4) Harry intends to complete a BSc degree. He has to take either Mathematics A or Physics A in his first year. If he takes Mathematics A, he can take chemistry A or Mathematics B in His second year. If he takes Physics A, he has to take Mathematics A in his second year. When Harry has to make a choice between two subjects both are likely to be chosen 1. Draw a decision tree to illustrate the above situation. 2. What is the probability that he will take Mathematics A during the two years? 3. What is the probability that he will take Mathematics A and B during the two years? [6 [2 (2
The overall probability that Harry will take Mathematics A during the two years is (0.5 * 0.5) + (0.5 * 1) = 0.75
The probability that Harry will take Mathematics A and B during the two years is (0.5 * 0.5) = 0.25
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The probability that Harry will take Mathematics A in his first year is 50%. If he takes Mathematics A in his first year, there is a 50% chance he will take it again in his second year. If he takes Physics A in his first year, he has to take Mathematics A in his second year. So the overall probability that Harry will take Mathematics A during the two years is (0.5 * 0.5) + (0.5 * 1) = 0.75The probability that Harry will take Mathematics A and B during the two years is (0.5 * 0.5) = 0.25To learn more about Probability, Visit
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55% of the fish in a pond are goldfish,
10/3 of the fish are perch and the rest of the fish are sticklebacks.
Write the ratio of goldfish to perch to sticklebacks in this pond in its simplest form.
Answer:
If 55% of the fish in the pond are goldfish, that would be 55/100 of the total number of fish. To express this as a fraction in its simplest form, we would divide the numerator and denominator by the greatest common divisor, 5. So, 55/100 simplifies to 11/20.
10/3 of the fish in the pond are perch, which in its simplest form is already in the form of 10/3.
The rest of the fish are sticklebacks, meaning the total number of goldfish, perch, and sticklebacks must add up to 100%. Therefore, to find the ratio of sticklebacks to goldfish and perch, we can subtract the percentage of goldfish and perch from 100%.
100 - 55 - (10/3) = 100 - 55 - 10/3 = 100 - 55 - (10/3) = 100 - 55 - (10*3/3) = 100 - 55 - 10 = 35.
So the ratio of goldfish to perch to sticklebacks in this pond is 11/20: 10/3: 35/100 in its simplest form.
Step-by-step explanation:
Evaluate geometric series sigma1^12 10×4^n-1
The value of the sigma notation is 55924050
How to evaluate the sigma notationFrom the question, we have the following parameters that can be used in our computation:
sigma1^12 10×4^n-1
Express properly
So, we have the following representation
[tex]\sum^{12}_{1} 10*4^{n-1[/tex]
The sum of the geometric series can be calculated using the formula:
S = a(1 - r^n)/(1 - r)
From the sigma notation, we have the following parameters
a = 10,
r = 4
n = 12.
Substituting these values, we get:
S = 10 * (1 - (4)^12) / (1 - 4)
Evaluate the expression
S = 55924050
Hence, the sum is 55924050
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answer the following
The slope of the line is -20
How to find the slope of the graph of a line?The slope of a line is a measure of how steep the line is. It is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The formula for the slope of a line is:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of two distinct points on the line.
From the graph, you can pick any two points. That is:
x1 = 0, y1 = 120 and x2 = 4, y2 = 40
m = (y2 - y1) / (x2 - x1)
m = (40- 120) / (4 - 0)
m = -80/4
m = -20
Thus, the slope is -20
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the lengtjs of the three sides of a traigle nor necessarlity a right trianglw are 2.92 m, 7.67 m, 8.82 m what is the cosine od the angle opposite the sidw of 8.82 m
The cosine of the angle opposite the side of length 5.64 meters is 0.4536.
In a triangle, the cosine of the angle opposite a side is given by the formula:
cos(angle) = (a^2 + b^2 - c^2)/(2ab) where a, b, and c are the lengths of the sides of the triangle and angle is the angle opposite the side of length c. Given the side lengths of the triangle as 3.18 meters, 7.82 meters and 5.64 meters, the side opposite angle we want to find is 5.64 meters.
so we can use the above formula and substitute the values,
cos(angle) = (3.18^2 + 7.82^2 - 5.64^2)/(23.187.82) = 0.4536
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This funnel is in the shape of a cone.
Determine the volume of the following cone.
The height of the cone is 20 cm and the R is 5 cm
Answer:
Exact volume: 500π/3 cm³
Approximate volume: 523.6 cm³
Step-by-step explanation:
For a cone,
V = (1/3)πr²h
V = (1/3)π(5 cm)²(20 cm)
V = 500π/3 cm³ ≈ 523.6 cm³
Find the diameter of a circle whose circumference is 62.8 feet. Use 3.14 for pie.
a. 18
b. 22
c. 20
d. 21
The diameter of the circle whose circumference is 62.8 feet is 20 ft, thus the correct option is C.
How to find the diameter of the circle?Remember that for a circle of diameter D, the circumference is given by the formula:
C = pi*D
Where pi = 3.14
Here we know that the circumference is 62.8 feet, then we can rewrite:
62.8 feet = 3.14*D
Now we can solve that equation for D, then we will get:
D = 62.8ft/3.14 = 20ft
The diameter is 20 ft, thus, the correct option is C.
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Use the properties of exponents to generate an expression equivalent to each expression.
[tex]2^(3t+4)[/tex]
The expression equivalent to the expression 2(3t + 4) is 6t + 8
How to determine the expression equivalent to each expression.From the question, we have the following parameters that can be used in our computation:
2(3t + 4)
To start with, we need to open the bracket of the expression
so, we have the following representation
2 * 3t + 2* 4
Evaluate the products
6t + 8
hence, the equivalent expression is 6t + 8
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PLEASE HURRY!!!! FOR 30 POINTS!!
Mr. Snow made snacks in separate gift bags. He gave one each to the 536 sixth-grade students going on the field trip. Then he gave 30 bags to the students in Mrs. Bond’s class for decorating the trophy cases. Next he gave 25 to the students in Mrs. Fuller’s class for helping during the school play. Mr. Snow had 3 snacks left. How many snacks did he make?
A . 600 snacks
B. 596 snacks
C. 594 snacks
D. 584 snacks
5x - 4y = 27; - 2x + y = 3
Answer: x=-13, y=-23
Step-by-step explanation:
y in terms of x
-2x+y=3
y=3+2x
Substitute in other equation:
5x-4(3+2x)=27
5x-12-8x=27
-3x=39
x=39/-3
x=-13
Solve for y, substitute for x:
-2(-13)+y=3
26+y=3
y=-23