Total number of marbles is 5 + 7 + 29 = 41.
Your expected profit or loss of you play this game $0.17 loss?
The given parameters are
2 gold marbles,
7 silver marbles,
and 29 black marbles
Also you win $4, if it is silver, you win $2. If it costs $1 to play
Event P(Event) Net Winnings P(Event) * Net Winnings
Gold 5/41 4 - 1 = 3 15/41
Silver 7/41 2 - 1 = 1 7/41
Black 29/41 -1 -29/41
sum -7/41 = $0.17 loss
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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.4 mmHg (millimeters of mercury) for a sample of size 686 and a sample standard deviation 5.5 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 90% confidence.
What is the 90% confidence interval to estimate the population mean? Round your answer to one decimal place.
Answer:
{30.1,30.7}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{90\%}=30.4\pm1.645\biggr(\frac{5.5}{\sqrt{686}}\biggr)\\\\CI_{90\%}\approx30.4\pm 0.3\\\\CI_{90\%}=\{30.1,30.7\}[/tex]
Thus, we are 90% confident that the true amount of mmHg that is lowered will be between 30.1 and 30.7 mmHg.
Which one of the following items is not necessary in preparing a statement of cash flows?
O Determine the cash provided by operations
O Determine cash from financing and investing activities
O Determine the cash in all bank accounts
Determine the change in cash
The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
What is meant by statement cash flows?In financial accounting, a cash flow statement, often called a statement of cash flows, is a financial statement that breaks down the analysis into operating, investing, and financing operations. It illustrates how changes in balance sheet accounts and income effect cash and cash equivalents.
A cash flow statement lists all of an organization's cash inflows from current operations and outside investment sources. The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
Functionally speaking, cash flows are categorized according to the nature of the underlying transaction. The statement's main goal is to give pertinent details about the agency's cash inflows and outflows during a given time period.
Therefore, the correct answer is option d) Determine the change in cash.
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A local high school has 1,152 students with 391 freshmen, 351 sophomores, 208 juniors, and 202 seniors. What is the
relative frequency of sophomores at this high school?
The relative frequency of sophomores at this high school is 39/128.
How to find the relative frequency?
Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).
We are given that;
Total students=1152
Freshmen=391
Sophomores=351
Juniors=208
Seniors=202
Now, to find frequency of sophomores
=number of sophomores/total number of students
=351/1152
=117/384
=39/128
Therefore, the relative frequency will be 39/128.
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That are a valid decomposition of c (x )such that c equals f ring operator g g (x )equals x squared f (x )equals cube root of x plus 1 end root g (x )equals x squared plus 1 f (x )equals cube root of x g (x )equals x plus 1 f (x )equals cube root of x squared end root g (x )equals cube root of x plus 1 f (x )equals x squared
By using the composition of functions, we can find valid decompositions of c(x) using f(x) = [tex](x+1)^{1/3}.[/tex] and g(x) = x²
A function is a rule that takes an input value and produces an output value.
One way to do this is to use the composition of functions. The composition of two functions f(x) and g(x) is denoted as f(g(x)). This means that we first apply g(x) to the input, and then apply f(x) to the output of g(x). In other words, we first evaluate g(x), and then plug that result into f(x) to get the final output.
Using this concept, let's look at the first set of functions. We are given
=> c(x) = f ◦ g (x) = (x²) f(x) = [tex](x+1)^{1/3}.[/tex]
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x², and f(x) = [tex](x+1)^{1/3}.[/tex] This is a valid decomposition of c(x).
Similarly, in the second set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x² + 1.
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x² + 1, and [tex](x+1)^{1/3}.[/tex] This is also a valid decomposition of c(x).
In the third set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x + 1, and f(x) = [tex](x^2)^{1/3}=x^{2/3}[/tex]
This is another valid decomposition of c(x).
Finally, in the fourth set of functions, we have
=> c(x) = f ◦ g (x) = x² g(x) = [tex](x+1)^{1/3}[/tex], and f(x) = [tex]x^{2/3}[/tex].
This is yet another valid decomposition of c(x).
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A function is given.
g(x) =
4
x + 5
; x = 0, x = h
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
A function is given net change and the average rate of change between the given values of the variable.
A. = - [tex]\frac{4h}{7h + 49}[/tex]
B. = - [tex]\frac{4}{7h + 49}[/tex]
What exactly is a sample average rate?Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.
According to given information:a) The net change is just the difference between g(h) and g(0). This is found below.
g(h) - g(0) = [tex]\frac{4}{h + 7}[/tex] - [tex]\frac{4}{0 + 7}[/tex]
= [tex]\frac{28 - 4h -28}{7h + 49}[/tex]
= - [tex]\frac{4h}{7h + 49}[/tex]
b) The average rate of change is the net change divided by the length of the interval. This is:
[tex]\frac{g(h) - g(0)}{h - 0}[/tex] = - [tex]\frac{{4h}/{7h + 49}}{h - 0}[/tex]
= - [tex]\frac{4}{7h + 49}[/tex]
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Since Mars is smaller than Earth, a projectile near the surface of Mars accelerates downward at a rate of only 3.8 meters per second every second. Suppose that an astronaut on the surface of Mars throws a ball upward at time t=0 such that the ball reaches a maximum height of 15 meters. Let h(t) be the height of the ball in meters t seconds after being thrown. Using the method of scaling and shifting from In-Class Activity 9.A, derive a formula for h(t)
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
here, we have,
From the graph of the function h(t) = 1 + 4t - 1.86t²:
The maximum height the rock reaches 3.15 feet.
Time spent on air
= 2.38 - (-0)
= 2.38 seconds
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds.
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Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 80 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.33?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's
approach and calculations.
(Enter your answer as a number accurate to 4 decimal places.)
The probability that the sample proportion is less than 0.33 is approximately 0.7422.
How to model sample proportion?The sample proportion of first-time customers can be modeled by a normal distribution with mean p, the true proportion of first-time customers, and standard deviation [tex]\sqrt{\frac{p(1-p)}{n}}[/tex], where n is the sample size.
In this case, p = 0.32, n = 80, and we want to find [tex]P(\hat{p} < 0.33)[/tex].
The standardized version of [tex]\hat{p}[/tex] is given by:
[tex]z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Substituting the values, we get:
[tex]z = \frac{0.33-0.32}{\sqrt{\frac{0.32(1-0.32)}{80}}} \approx 0.6579[/tex]
Using a standard normal distribution table (or a calculator or statistical software), we find that the probability of z being less than 0.6579 is approximately 0.7422.
Therefore, the probability that the sample proportion is less than 0.33 is approximately 0.7422.
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Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]
A scientific model is used to predict the average global high
temperature on earth by anaylizing the data from previous
years. In 1940, the temperature was 55° F However, the
temperature has grown to 59.5° F in 1990.
A) Find an equation in the form T = ax + b, where x is the
number of years since 1940 and T is the average gobal high
temperture on Earth.
Answer:
chapter 1
Step-by-step explanation:
Which represents the solution to the inequality 5.1(3+2.2x)>-14.25-6(1.7x+4)?
X=<-2.5
x>2.5
(-2.5,~)
(-~,2.5)
Step-by-step explanation:
Hope it helps :) #CarryOnLearning
Write this ratio as fraction in lowest terms. 8.64 to 37.76
The ratio 8.64 : 37.76 as a fraction will be 27/118.
What precisely is ratio?
Ratios and proportions are typically described using fractions. When a fraction is presented as a:b, a ratio is shown, whereas a percentage suggests that two ratios are equal. In this case, a and b can be any two numbers. The ratio and proportion are two essential notions that serve as a foundation for understanding other concepts in mathematics and science.
In our daily lives, we apply the notion of ratio and proportion, such as in business when dealing with money or in cooking.
As a consequence, when b is greater than zero, the ratio specifies the connection between two variables, such as a:b. The 2:4 ratio, for example, is written as 2:4 = 1:2.
Now,
Given ratio is 8.64 : 37.76
we can write this as 8.64/37.76
=864/3776
=432/1888
=216/944
=54/236
=27/118
Hence,
The ratio 8.64 : 37.76, as a fraction will be 27/118.
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please thank you mwaaaaaaaaaaaaa
The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is 301.44 square inches.
What is perimeter and area enclosed in circle?
A circle is also defined by two properties: area and perimeter. The formulas for both the measures of the circle are given by; Area of a circle = πr². The perimeter of a circle = 2πr.
Let's call the center of the circle O and the endpoint of the arc A. Let's also call the endpoint of the chord that defines the segment B. Then we have an isosceles triangle OAB, where OA = OB = 24 inches.
1) The perimeter of the segment is equal to the length of the arc plus the length of the chord. To find the length of the arc, we can use the formula:
Arc length = (Ф / 360) * 2πr,
where Ф is the measure of the angle in degrees, r is the radius (which is 24 inches in this case), and π is pi.
In this case, the measure of the angle is 60°, so the length of the arc is:
Arc length = (60 / 360) * 2π * 24 inches
Arc length = (1/6) * 2π * 24 inches
Arc length = 4π inches
To find the length of the chord, we can use the formula:
Chord length = 2r * sin(Ф/2), where r is the radius and Ф is the measure of the angle in radians.
First, we need to convert the angle measure from degrees to radians:
60° = 60 * (π / 180) radians = π / 3 radians
Now, we can find the length of the chord:
Chord length = 2 * 24 * sin(π / 6)
Chord length = 24 * 2 * sin(π / 6)
Chord length = 24 * √3 inches
Finally, we can add the length of the arc and the chord to find the perimeter:
Perimeter = 4π + 24 * √3
Perimeter = 4π+41.57
Perimeter = 54.13 inches
2) To find the area of the segment, we can use the formula:
Area = (Ф/ 360) * πr², where Ф is the measure of the angle in degrees and r is the radius.
In this case, the measure of the angle is 60°, so the area of the segment is:
Area = (60 / 360) * π * 24² square inches
Area = (1/6) * π * 576 square inches
Area = 96π square inches
Area = 301.44 square inches
So, The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is301.44 square inches.
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There are 32 computers in a computer lab—some are laptops, and some are desktops. If there
are 8 more laptop computers than desktop computers, how many of each type of computer are
in the lab?
Answer:
There are 12 desktop computers and 20 laptop computers.
Step-by-step explanation:
32:2=16
8:2=4
16-4=12
16+4=20
Which choices are equivalent to the expression below?
Check all that apply.
√24
A. 4.√6
B. 2 √6
C. √4.6
D. 24
E. 8.√6
F. √12
The value equivalent to the expression is (2)√6 and option B is the correct answer.
What is prime factorization?Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.
the quantities that are multiplied to produce new quantities. For instance, the factors of 15 are 3 and 5, or 3 + 5 = 15.
The given expression is √24.
Find the prime factorization of 24:
2 | 24
2 | 12
2 | 6
3 | 3
| 1
Thus, √24 can be written as:
√24 = √(2)²(2)3
√24 = (2)√6
Hence, the value equivalent to the expression is (2)√6 and option B is the correct answer.
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A. 188.5in²
B. 94.25in²
C. 133.5in²
D. 149.25in²
Answer:B
Step-by-step explanation:
area of triangle is (10*11)/2=55
area of semicircle is
[tex]d=2r\\r=10/2=5\\s=\pi r^{2} /2=25\pi /2=39.25\\39.25+55=94.25[/tex]
Parallelogram ABCD is a rhombus. Side BC = 5cm and segment AO = 3.8cm
What is the measure of angle d₁°?
What is the tangent ratio of angle c₂?
Answer:
Let's call angle d₁ "θ". To find θ, we can use the Pythagorean theorem. The segment AO is the hypotenuse of a right triangle with sides BC/2 and AC/2 (since the rhombus is a parallelogram, opposite sides are equal).
AC/2 = (BC/2) / tan(θ)
So:
tan(θ) = AC/2 / (BC/2)
Plugging in the values we have:
tan(θ) = 3.8 / (5/2) = 3.8 / 2.5 = 1.52
Therefore,
θ = tan^(-1)(1.52) = 55.23°
The tangent ratio of angle c₂ is simply the tangent of the angle:
tan(c₂) = tan(90° - θ) = tan(90° - 55.23°) = tan(34.77°) = 1.52
So the tangent ratio of angle c₂ is 1.52.
Step-by-step explanation:
What is the size, in degrees, of the missing angle?
45
65°
The three graphs represent the progress of three runners in a 500-meter race.
The red solid line represents runner A. The purple dotted line represents runner B.
The blue dashed line represents runner C.
Options: Runner A, Runner B, Runner C, 0, 20, 55, 90.
The answers include the following:
Runner B ran at a constant rate throughout the race.Runner C stopped running for a while and it occurred between 20 to 55.Runner A also sprinted at different speeds.Runner A won the race.What is Speed?This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.
From the graph, we can deduce that Runner A won the race because it attained a greater distance when compared to the time for all the other runners.
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it is expected that over the next 10 years,the speed of personal computer will double every 18 months.calculate how much faster the speed of personal computer will be in 6 years time compared to now
Answer: Since the speed of personal computers is expected to double every 18 months, we can use exponential growth to calculate the increase in speed over time. We can start by finding the growth factor, which is equal to 2 raised to the power of the number of doublings. In this case, the number of doublings over 6 years can be calculated as follows:
6 years / 1.5 years = 4 doublings
So the growth factor is:
2^4 = 16
This means that the speed of personal computers will be 16 times faster in 6 years compared to now.
Step-by-step explanation:
state the next terms in the sequence of number 8, 4, 2, 1 -1/2
The next term in the sequence of number 8, 4, 2, 1, 1/2 is 1/4
How to determine the next term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
The sequence of number 8, 4, 2, 1 -1/2
Express properly
The sequence of number 8, 4, 2, 1, 1/2
The above definitions imply that we simply divide the previous term by 2 to get the current term
Using the above as a guide,
Next term = (1/2)/2
Evaluate
Next term = 1/4
Hence, the next term is 1/4
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Question 4 (10 points)
(03.06 MC)
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points
The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.
Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³
Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³
The volume of this cylinder is 1.5 times that of the cone
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What are the slopes and lengths?
Answer:
KL - slope 6/5 , length 7.8
LM - slope -5/6 , length 7.8
MN - slope 6/5 , length 7.8
NK - slope -5/6 , length 7.8
Step-by-step explanation:
square :3
You randomly draw once from this deck of cards.
4 6
1 6 9 4
8
1
1
2 6 7
What is the probability of not drawing an even number? Write your
answer as a fraction.
9
5
Answer:why not
Step-by-step explanation:that sa prrety nice ask
Answer: 5/8
Step-by-step explanation:
The probability of not drawing an even number can be calculated by finding the number of odd numbers in the deck and dividing by the total number of cards. In this deck, there are 5 odd numbers: 1, 1, 1, 7, and 9. The total number of cards is 8. Therefore, the probability of not drawing an even number is 5/8. The answer is written as a fraction as 5/8.
Please help quickly!
Using the rules for matrix multiplication we will see that a₁₂ = 144
How to find the element a₁₂?That would by the second element on the first row of the product matrix.
Remember how the product works, we will get:
a₁₂ = 24*2 + 32*3
a₁₂ = 48 + 96
a₁₂ = 144
The correct option is the last one.
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A 10-ft pendulum swings through an angle of 40°6'. What is the length of the arc that the tip of the pendulum travels? Round
intermediate calculations to 3 decimal places. Round your final answer to the nearest hundredth of a foot.
The length of the arc that the tip of the pendulum travels is approximately 7 feet.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
We can use the formula for the length of an arc of a circle to find the length of the arc that the tip of the pendulum travels:
Arc length = (angle/360) x 2πr
where: angle = the central angle (in degrees or radians) that the arc subtends and r = the radius of the circle
First, we need to convert the angle from degrees and minutes to decimal degrees.
There are 60 minutes in a degree, so:
40°6' = 40 + 6/60 = 40.1 degrees
Now we can plug in the values:
Arc length = (40.1/360) x 2π(10 feet)
Arc length = 6.99 feet
Hence, the length of the arc that the tip of the pendulum travels is approximately 7 feet.
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2. Чему равна разность? Сравните результаты.
Answer:
[tex] \frac {3}{8} + \frac{2}{8} = \frac{5}{8} = 1 \frac{3}{8} [/tex]
[tex] = \frac{5}{ \\ 8} = 1 \frac{3}{8} [/tex]
PLEASE HELP; BEEN STUCK ON THIS PROBLEM FOR A WHILE:
Answer:
been a while, so I'd check w someone else too, but hope this helps
Step-by-step explanation:
_____
which two integers is between /-83
The two integers that are between -83 and +83 are -82 and +82.
What is integers ?
In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.
There are multiple pairs of integers that are between -83 and 83.
Here are two examples:
-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -50 0 50 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -75 0 75 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.
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What are the line segments in this rectangle?
a rectangle with the vertices labeled Q, R, S, and T
Answer:
qr rs st qt are the line hope it helped
helpppp ASAP.
1. What is the height of the cone? Explain how you found the height. (4 points)
2. Now that you have the height of the cone, how can you solve for the slant height, s? (3 points)
3. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. (3 points)
1. The height of the cone is, 22.18 mm.
2. The slant height is, 28.14 mm.
3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
The volume of cone V = (1/3)πr²h
Given that,
The volume = 8792 mm³
1. by using the formula to solve for h,
we get h = (3V)/(πr²).
Plugging in the values given,
we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.
Therefore, the height of the cone is approximately 22.18 mm.
2. it is known that, from the Pythagoras theorem
s² = h² + r²,
where s is the slant height, h is the height, and r is the radius.
Plugging in the values we found in part 1,
we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².
Taking the square root of both sides, we get s ≈ 28.14 mm.
Therefore, the slant height is approximately 28.14 mm.
3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.
Using the value we found in part 2,
the length of the slant height is approximately 28.14 mm.
Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.
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