Answer:
Answer is a continuous random variable x the height of the function named the probability density function f(x)
Step-by-step explanation:
A continuous random variable takes infinite number of possible values.
example include height , weight amount of sugar in an orange time required to run a mile.
Continues random variable named probability function f(x).
The height of a function at a certain value of x in the case of a continuous random variable represents the probability density at that point, not the actual probability. The area under the curve of the function between two points gives the actual probability that x falls between those points. The total probability (the total area under the curve) is always 1.
Explanation:For a continuous random variable x, the height of the function at a certain value of x is named the probability density function f(x) which describes the probabilities for continuous random variables. The value does not represent a direct probability but the density of probability around that point, and the area under the curve between two given points gives the probability that x would fall between those points. This is represented by the notation P(c < x < d), where c and d are the boundaries of the interval.
It is essential to note that for any specific value of a continuous random variable, the probability is always 0, represented as P( x = c )= 0, which means the height of the function at a particular x does not represent the exact probability at that point but just the density.
The total probability of a continuous random function is always 1, thus, the total area under the probability density function curve equals one. And the value of the function at any given point can be less or greater than 1 given the function's shape and range.
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9/20
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0
nd
01
ations
02
O cannot be determined
are
00
e
100%
For this case we must find the solution of the following quadratic equation:
[tex]x ^ 2 + 5x + 7 = 0[/tex]
Where:
[tex]a = 1\\b = 5\\c = 7[/tex]
Then, the solution is given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Substituting the values:
[tex]x = \frac {-5 \pm \sqrt {5 ^ 2-4 (1) (7)}} {2 (1)}\\x = \frac {-5 \pm \sqrt {25-28}} {2}\\x = \frac {-5 \pm \sqrt {-3}} {2}[/tex]
By definition we have:[tex]i ^ 2 = -1[/tex]
[tex]x = \frac {-5 \pm \sqrt {3i ^ 2}} {2}\\x = \frac {-5 \pm i \sqrt {3}} {2}[/tex]
Thus, we have two complex roots.
Answer:
The equation has no real roots.
Vector V is in standard position and makes an angle of 50° with the positive x-axis. Its magnitude is 18. Write V in component form a, b and in vector component form ai + bj. (Round each answer to one decimal place.)
Answer:
11.57 units east, 13.79 units upwards
11.57i + 13.79j
Step-by-step explanation:
V = 18 units at an angle of 50° to the positive x-axis
In component Form, this is how each component is calculated
a = 18cos50° = 11.57 units east
b = 18sin50° = 13.79 units upwards
check if your answer is correct
[tex]\sqrt{11.57^{2} +13.79^{2} } = 18.0[/tex]
In vector component form ai + bj = 11.57i + 13.79j
Choose the best answer :
what percent of your pre-retirement earnings do most financial advisors say you’ll need to comfortably maintain your pre-retirement standard of living
• 60%
• 70%
• 80%
• 90%
Answer:
• 80%
Step-by-step explanation:
Consult your course reference materials.
Advice found on the Internet varies from 70% to 90%, depending on a number of factors. 70% has been a guide historically, but more recent advice favors higher numbers, it seems.
Organic Food Inc., a multinational company, relies on its media partner Radio Plus to regularly advertise its offers, sales, and new products. Radio Plus is invested in this relationship because it generates most of its revenue from advertising Organic Food's products. In this scenario, Radio Plus is Organic Food Inc.'s
Answer:
External stakeholder.
Step-by-step explanation:
Radio Plus is invested in this relationship because it generates most of its revenue from advertising Organic Food's products.
In this scenario, Radio Plus is Organic Food Inc.'s - external stakeholder.
External stakeholders are those individuals or companies that do not lie within a business itself, but these care about the business and are affected by the business's performance.
Please help me with this!!!!!!!!!!!!!
Answer:
download photomath
Step-by-step explanation:
I swear it would help you because it always help me.. just look carefully
Answer: x = 1,
y = 5
z = 2
Step-by-step explanation:
Adam and Brianna plan to install a new tile floor in a classroom. Adam works at a constant rate of 50 tiles per hour, and Brianna works at a constant rate of 55 tiles per hour. If the new floor consists of exactly 1400 tiles, how long will it take Adam and Brianna working together to complete the classroom floor?
Answer:
t≅13.33h
Step-by-step explanation:
Adam (A) works at constant rate of 50tiles/h
Briana (B) works at constant rate of 55tiles/h, this means that A=50 tiles per hour and B=55 tiles per hour, then A+B = 105tiles/h together, but the floor consists of 1400tiles, so if 105 tiles are installed in one hour, then 1400 tiles in how long they will be installed?
t = 1400tiles*h/105tiles≅ 13.33 h
I need help with this question.
Answer:
[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]
Step-by-step explanation:
Given two vectors a and b,we are rquired to find the angle between them.
a=(8,7);b=(7,0).
Angle between two vectors can be found by dot product of them.
If a and b are two vectors then the dot product of them is given by|a||b|cos(α).
Where α is the angle between the vectors a and b.
Now [tex]|a|=\sqrt{113}\text{ } and\text{ } |b|=\sqrt{49}[/tex]. and [tex]a.b=8\ times 7+7\times 0[/tex] =56.
Now cosα=[tex]\frac{8}{\sqrt{113} }[/tex] so α= cosine inverse of that.
∴α=
[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]
A manufacturer wants to estimate the proportion of defective items that are produced by a certain machine. a random sample of 50 items is selected. which excel function would not be appropriate to construct confidence interval estimate?a. Countifb. Norm.s.invc. Stdevd. all of these answer are correct
Answer:
c. Stdev
Step-by-step explanation:
Excel stdev function is not appropriate to construct confidence interval estimate, because the estimation of the proportion of defective items that are produced by a certain machine has binomial distribution.
stdev fuction is used for calculating standard deviations where sample has more than two different values. (multinomial)
Norm.s.inv function calculates inverse of the standard normal cumulative distribution, and countif counts the number of cells that meet a criterion. Both functions are used to construct confidence interval estimate
Prove that y=x² at x=0 has both a local and global minimum using first derivative test. I can prove it with a graph looking at it visually but how would you prove it with written words.
[tex] \frac{d}{dx} {x}^{2} = 2x \\ x = 0 \\ 2 \times 0 = 0[/tex]
When the derivative equals zero, that point is either the maximum or minimum.
[tex] {x}^{2} \geqslant 0[/tex]
The smallest real value of x² is 0, which is at x = 0.
Hence, x² at x = 0 has both a local and global minimum.
Step-by-step explanation:
y = x²
Find the first derivative:
dy/dx = 2x
Find the critical values by setting dy/dx to 0:
0 = 2x
x = 0
Evaluating the first derivative before and after x=0, we see that dy/dx changes signs from negative to positive.
x < 0, dy/dx < 0
x > 0, dy/dx > 0
That means x=0 is a local minimum.
To find the global minimum, we need evaluate the function at x=0 and at the end points.
x = -∞, y = ∞
x = 0, y = 0
x = ∞, y = ∞
So x=0 is also the global minimum.
The size of each interior angle of a regular polygon with n n sides is 140° Work out the size of each interior angle of a regular polygon with 2n sides.
Answer:
160°
Step-by-step explanation:
The corresponding exterior angle is 180°-140° = 40°. When the polygon has 2n sides, that angle will be cut in half to 20°. The interior angle of that polygon will be 180°-20° = 160°.
_____
The exterior angles always sum to 360°. Since their sum is a constant, doubling the number of them will cut their measure in half.
To find the size of each interior angle in a regular polygon with 2n sides, when n sides gives 140° each, we use the interior angle formula (n-2) * 180 / n. First, we find n using 140 = (n-2) * 180 / n and substitute n into ((2*n) - 2) * 180 / (2*n) for the result.
Explanation:The size of each interior angle in a regular polygon is calculated using the formula (n-2) * 180 / n, where n is the number of sides. Given that a polygon with n sides has an interior angle of 140°, we can use this formula to calculate the size of each interior angle in a regular polygon with 2*n sides. The calculation would be: ((2*n) - 2) * 180 / (2*n).
Therefore, to calculate the size of each interior angle in a regular polygon with 2*n sides - if n sides gives 140° each, we must first calculate n using 140 = (n-2) * 180 / n and then substitute n in ((2*n) - 2) * 180 / (2*n) to get the result.
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Use logs to determine the number of years until the population drops to 15,390 organisms. Round answer to 2 decimal places.
Answer:
4.47 years
Step-by-step explanation:
Fill in the numbers and solve for t.
P = a·b^t
15390 = 19000·0.954^t
15390/19000 = 0.954^t . . . . . divide by 19000
0.81 = 0.954^t . . . . . . . . . . . . . simplify
log(0.81) = t·log(0.954) . . . . . . take the log
t = log(0.81)/log(0.954) . . . . . . divide by the coefficient of t
t ≈ 4.47
It will take about 4.47 years for the population to drop to 15390 organisms.
_____
A graphing calculator can be another way to solve a problem like this.
The product of two consecutive odd integers is 72. Write a quadratic equation to find the integers,
Answer:
[tex]x^2 + x - 72 = 0[/tex]
Explanation:
We are given product of two consecutive odd integers is equal to 72.
Let one integer be x , then since these are consecutive and odd so the other integer will be equal to x + 1.
Their product is equal to 72. So,
x * (x + 1) = 72
=> [tex]x^2 + x = 72[/tex]
=> [tex]x^2 + x - 72 = 0[/tex] is the required quadratic equation.
Carson bought two loaves of bread and one dozen eggs at the grocery store yesterday he paid a total of $6.09.If one dozen of eggs cost $1.79,how much is a loaf of bread?
Answer: $4.30
Step-by-step explanation: if you take 6.09 and subtract 1.79 you will get $4.30
I need all the questions answered.Show Work
Answer:
5 i) Space occupied by 1 ball = 137.26 cubic centimeters
5 ii) Space occupied by 6 tennis balls = 823.56 cubic centimeters
6 i) 19.2 centimeters
6 ii) 12.8 centimeters
6 iii) 6.4 centimeters
6 iv) 1572.86 cubic centimeters
7. 749.3 cubic centimeters
Step-by-step explanation:
5.
i)
A tennis ball is in a shape of a sphere. The space occupied by 1 tennis ball is the volume of a sphere. The formula is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where
V is the volume and r is the radius (half of diameter)
Given diameter is 6.4 , the radius would be:
r = 6.4/2 = 3.2
Now, we substitute and find the volume:
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (3.2)^3\\V=137.26[/tex]
Space occupied by 1 ball = 137.26 cubic centimeters
ii)
We found space occupied by 1 ball, so space occupied by 6 balls would be 6 times that. So that would be:
Space occupied by 6 tennis balls = 137.26 * 6 = 823.56 cubic centimeters
6.
i)
The length of the box would be 3 diameters lined up. Since the length comprises of 3 balls side by side, we can say that 6 diameters would make up the length of the box, so:
diameter = 6.4
3 diameters = 6.4 * 3 = 19.2 centimeters
ii)
Now, we want the width of the box. That is 2 tennis balls lined up (as seen in the picture). That would be 2 diameters. so:
diameter = 6.4
2 diameters = 6.4 * 2 = 12.8 centimeters
iii)
The height of the box would be the height of 1 balls (see pic). That would be just 1 diameter of the ball. Given:
Diameter = 6.4 cm
So,
Height = 6.4 cm
iv)
The box is a rectangular prism. Which has a capacity (volume) formula as:
Volume = length * width * height
In the first 3 parts of this problem, we found each. Let's multiply each out to find the capacity of the box.
Volume = 19.2 * 12.8 * 6.4 = 1572.86 cubic centimeters
7.
The amount of empty space in the box is the volume of the rectangular box MINUS the volume of all the 6 balls. We have already found:
Volume of Box = 1572.86
Volume of 6 balls = 823.56
Hence,
Empty Space = 1572.86 - 823.56 = 749.3 cubic centimeters
Assume that a hat contains four bills: a $1 bill, a $5 bill, a $10 bill and a $20 bill. Two bills are to be selected at a random with replacement. find the probability that
a) both bills are $1 bill if the first selected is a $1 bill
b) both bills have a value greater than a $5 bill if the second bill is a $10 bill
Answer:
a)1/4
b)1/2
Step-by-step explanation:
a) The selection is with replacement, then we already have 1 $ bill and in the hat again the four bills. What is the probability of select 1$ bill ? well it is 1/4.
The point here is, replacement condition make the second trial totally independent of the first one
b)Following the same reasoning now we have selected a 10 $ bill, and we have two possibles positive outcome a 10 $ and a 20 $ bill and a total of 4 outcomes th th probability is 1/2
The probabilities are:
a) 1/16
b) 1/8.
How to find the probabilities?
We assume that all the bills have the same probability of being randomly selected.
a) Then the probability of randomly selecting a $1 bill is equal to the number of $1 bills on the hat divided by the total number of bills.
There is one $1 bill on the hat, and 4 bills in total, so the probability is:
p = 1/4.
Then you return the $1 bill to the hat and want to draw it again, with the same probability as before.
q = 1/4.
The joint probability is the product of the individual probabilities, so we have:
P = p*q = (1/4)*(1/4) = 1/16.
b) There are 2 bills that have a larger value than $5, then the probability for the first draw is:
p = 2/4
For the second draw, we must get the $10 bill, and the probability of getting it is:
q = 1/4.
The joint probability is:
P = p*q = (2/4)*(1/4) = 1/8.
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A chi-square test for independence is used to evaluate the relationship between two variables. If both variables are classified into two categories, then what is the df value for the chi-square statistic?
The degrees of freedom (df) value for a chi-square test for independence is calculated using the formula: df = (number of columns - 1) x (number of rows - 1).
Explanation:The degrees of freedom (df) value for a chi-square test for independence when both variables are classified into two categories can be calculated using the formula:
df = (number of columns - 1) x (number of rows - 1)
For example, if we have a contingency table with 2 columns and 2 rows, the df value would be:
df = (2 - 1) x (2 - 1) = 1 x 1 = 1
There were 128 threatened species of animals and 144 threatened species of plants in the United States in 2001. Write the ratio of threatened species of animals to threatened species of plants as a fraction in simplest form.
If you go by division is is eight to nine.
Final answer:
The ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed in simplest form, is 8:9 or 8/9 after dividing both numbers by their greatest common divisor, which is 16.
Explanation:
The question asks for the ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed as a fraction in simplest form. To find the ratio, we divide the number of threatened animal species by the number of threatened plant species. The given numbers are 128 threatened animal species and 144 threatened plant species.
To simplify the ratio 128:144, we divide both numbers by their greatest common divisor (GCD). The GCD of 128 and 144 is 16. Thus, dividing both sides of the ratio by 16, we obtain:
128 ÷ 16 = 8
144 ÷ 16 = 9
The simplified form of the ratio is 8:9, or written as a fraction 8/9.
A child throws a ball with a speed of 5 feet per second at an angle of 73 degrees with the horizontal. Express the vector described in terms of i and j.
Answer:
v = 5cos(73°)i +5sin(73°)j
Step-by-step explanation:
The components of the velocity vector are ...
horizontal (i direction): 5·cos(73°)
vertical (j direction): 5·sin(73°)
Then the velocity vector is the sum of these component vectors:
v = 5cos(73°)i +5sin(73°)j
A school has two computer labs Each lap has 30 computers a total of six computers in the school or not working which expression can be used to find the number of working computers in the school
Answer:
Step-by-step explanation:
A school has two computer labs and each lan has 30 computers. This means that the total number of computers is the sum of the number of computers in each lab
Total number of computers = 30+30 = 60
A total of six computers in the school or not working.
The expression that can be used to find the number of working computers in the school will be
Let the number of computers that are working be x
the number of computers that are working is total number of computers minus the number of computers that are not working be
The expression that can be used to find the number of working computers in the school will be
x = 60 - 6
x = 54
Find the critical values: a. Determine the critical value z????/2 that corresponds to a level of confidence of 87%. (2 pts). b. Find the critical t-value t????/2 that corresponds to 92% confidence and n = 15. (2 pts). c. Determine the critical value for a left-tailed test of a population mean at the α = 0.025 level of significance based on a sample size of n = 18. (2 pts) d. Find the critical value for a two-tailed test of a population proportion with α = 0.08. (2 pts)
Answer:
a) [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]
b) [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]
c) [tex]t_{\alpha/2}=-2.11[/tex]
d) [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]
Step-by-step explanation:
Part a
On this case the confidence is 87% or 0.87 so the significance level is [tex]\alpha=1-0.87=0.13[/tex] and [tex]\alpha/2 =0.065[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.
We need values a,b on the normal standard distribution such that:
[tex]P(Z<a)=0.065[/tex] or [tex]P(Z>b)=0.065[/tex] and in order to find it we can use the following code in excel:
"NORM.INV(0.065,0,1)" or "NORM.INV(1-0.065,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]
Part b
On this case the confidence is 92% or 0.92 so the significance level is [tex]\alpha=1-0.92=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.
First we need to calculate the degrees of freedom given by:
[tex]df=n-1=15-1=14[/tex]
We need values b,c on the t distribution with 14 degrees of freddom such that:
[tex]P(t_{(14)}<b)=0.04[/tex] or [tex]P(t_{(14)}>c)=0.04[/tex] and in order to find it we can use the following code in excel:
"T.INV(0.04,14)" or "T.INV(1-0.04,14)", and we see that the critical values [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]
Part c
The significance level is [tex]\alpha=0.025[/tex] and is a left tailed test. On this case we know that is a left tailed test so then we have just one critical value.
First we need to calculate the degrees of freedom given by:
[tex]df=n-1=18-1=17[/tex]
We need a value c on the t distribution with 17 degrees of freddom such that:
[tex]P(t_{(17)}<c)=0.025[/tex], and in order to find it we can use the following code in excel:
"T.INV(0.025,17)", and we see that the critical values [tex]t_{\alpha/2}=-2.11[/tex]
Part d
The significance level is [tex]\alpha=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we know that w ehave a two tailed proportion test, so we will have two critical values.
We need values a,b on the normal standard distribution such that:
[tex]P(Z<a)=0.04[/tex] or [tex]P(Z>b)=0.04[/tex] and in order to find it we can use the following code in excel:
"NORM.INV(0.04,0,1)" or "NORM.INV(1-0.04,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]
a. The critical value z????/2 for a level of confidence of 87% is approximately 1.475. b. The critical t-value t????/2 for a 92% confidence level and n = 15 is approximately 1.761. c. The critical value for a left-tailed test at α = 0.025 and n = 18 is approximately -2.101. d. The critical value for a two-tailed test of a population proportion with α = 0.08 is approximately 1.755.
Explanation:a. To find the critical value z????/2 for a level of confidence of 87%, we need to find the z-score that leaves an area of 0.87 in the center. This means the area in each tail is (1 - 0.87) / 2 = 0.065. Using a z-table or calculator, the critical value is approximately 1.475.
b. For a 92% confidence level and a sample size of 15, we need to find the critical t-value t????/2. First, we determine the degrees of freedom, which is n - 1 = 15 - 1 = 14. Using a t-table or calculator, the critical t-value is approximately 1.761.
c. For a left-tailed test at the α = 0.025 level of significance and a sample size of 18, we need to find the critical value. Since the level of significance is α = 0.025, the area in the left tail is 0.025. Using a t-table or calculator, the critical value is approximately -2.101.
d. For a two-tailed test of a population proportion with α = 0.08, we need to find the critical value. Since we have a two-tailed test, we divide α by 2 to get 0.08 / 2 = 0.04. Using a z-table or calculator, the critical value is approximately 1.755.
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A bank Certificate of Deposit is a: a Cash deposit in a savings account that earns interest b Certificate for deposits that are issued for half the face value c Savings instrument that requires a deposit for a period of time during which there is a penalty for withdrawals d Savings instrument that requires a deposit for a period of time during which the saver can withdraw money from the plan at any time without a penalty
Answer:
C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.
Step-by-step explanation:
A Certificate of Deposit is a financial savings product offered by banks. A Certificate of Deposit, also known as a CD, can be obtained from a bank or a credit union.
CDs have a greater interest rate return than savings accounts due the conditions that savings from a CD cannot be withrawn for a fixed period of time. The higher the return the longer the period the savings cannot be withdrawn or the higher the intital investment.
CDs are insured by the Federal Deposit Insurance Corporation (FDIC) and if savings are not needed for a known period of time offer a better return than a savings account.
Answer:
C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.
Which graph represents an exponential function? On a coordinate plane, a line curves upwards gradually. On a coordinate plane, a curve decreases, changes directions, and then decreases again. On a coordinate plane, a line is level and then curves upwards rapidly. On a coordinate plane, 2 curves mirror each other in quadrants 1 and 3.
The options are not clear but we can describe exponential function as follows
Exponential function are of the form
[tex]y = b^x \; where\; b >0 = Exponentially\; Growing\\b<0 \; Exponentially\; Decaying \\\\x = Exponent[/tex]
The exponential functions are curved upwards gradually (figure attached )
Figure 1 (graph attached ) Shows the graph of function
[tex]y = 2^x[/tex]
We can conclude that exponential function is a monotonous function and
depending upon the value of b the exponential function is either continuously increasing or continuously decreasing
[tex]y = -3^x[/tex]
as shown by Figure 2 (figure attached )
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Answer:
It's D
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Assume 2 kg of apples is 1 dozen and that each apple has 8 seeds. How many apple seeds are in 14 kg of apples?
Answer:
There are 672 seeds in 14 kg of apples
Step-by-step explanation:
2 kg of apples = 1 dozen
1 dozen = 12 apples
So, 2 kg of apples =12 apples
1 kg of apples = [tex]\frac{12}{2} apples[/tex]
1 kg of apples = [tex]6 apples[/tex]
14 kg of apples =[tex]6 \times 14=84 apples [/tex]
Each apples has 8 seeds
So, 84 apples has seeds = [tex]8 \times 84= 672 seeds[/tex]
Hence there are 672 seeds in 14 kg of apples
Apple seeds are in 14 kg of apples is mathematically given as
672 seeds
Apple seeds are in 14 kg of applesQuestion Parameters:
2 kg of apples is 1 dozen and that each apple has 8 seeds. How many apple seeds are in 14 kg of apples
Generally the equation for the is mathematically given as
2 kg of apples = 1 dozen
1 dozen = 12 apples
Hence
1 kg of apples = 12/2
1 kg of apples = 6
14 kg of apples = 6*14
84 apples has seeds = 8*84
84 apples has seeds = 672
There are 672 seeds in 14 kg of apples
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Jordan flipped a coin 490 times. Which of the following would be a good estimate of the number of times the coin landed on heads?
A. 440
B. 230
C. 345
D. 170
Answer:
230.
Step-by-step explanation:
You have a 50% chance to get heads or tails. So that's half of 490, which is 245. It says estimate, so that means a relative guess. 230 would be the closest.
Final answer:
To estimate the number of times a coin flipped 490 times lands on heads, one should expect approximately half of the flips to be heads, which is about 245. Thus, option B. 230 is the closest estimation.
Explanation:
The question deals with the probability of outcomes when flipping a coin multiple times. When you flip a coin, the probability of it landing on heads is 50 percent each time, irrespective of previous outcomes. Thus, if you flip a coin 490 times, a good estimate for the number of times it will land on heads is roughly half of 490, which is 245. Therefore, the best estimate from the given options would be B. 230, as it is the closest to 245.
Jack keeps his music cd stuck in plastic boxes 3/8 inch thick.Use the method taught in this lesson to find the number of boxes in a stack 6 inches tall
A method for determining whether a critical point is a minimum, maximum, or neither using the slope of the curveA) First Derivative TestB) Absolute MaximumC) AccelerationD) Concavity
Answer:
a. First derivative
Step-by-step explanation:
To determine the nature of the stationary points:
Either Find dy/dx or d2y/dx2
If the result is: positive—the point is a minimum one; negative—the point is a maximum one; zero—the point is a point of inflexion
or
Determine the sign of the gradient of the curve just before and just after the stationary points.
If the sign change for the gradient of the curve is: positive to negative—the point is a maximum one; negative to positive—the point is a minimum one; positive to positive or negative to negative— the point is a point of inflexion
A method for determining whether a critical point is a minimum, maximum, or neither using the slope of the curve is the First Derivative Test (Letter A).
First Derivative TestCritical points represent the values of x for that f '(x) is zero or the derivative doesn't exist. Therefore, they represent the only places where a function can have a local minimum, maximum or neither using the slope of the curve. See the rules for this method:
If f′(x) changes from positive to negative at c, then f(c) is a local maximum.If f′(x) changes from negative to positive at c, then f(c) is a local minimum.If f′(x) does not change sign at c, then f(c) is neither a local maximum or minimum.Read more about the First Derivative Test here:
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Aurora is selling tickets to a carnival. The function f(x) = 0.5x represents the amount of money Aurora earns per ticket, where x is the number of tickets she sells. The function g(x) = 8x represents the number of tickets Aurora sells per hour, where x is the number of hours she works. Find f(g(x)), and explain what it represents.
a. f(g(x)) = 4x, which represents the money Aurora made in dollars per hour
b. f(g(x)) = 4x, which represents the number of tickets Aurora sold per hour
c. f(g(x)) = 16x, which represents the money Aurora made in dollars per hour
d. f(g(x)) = 16x, which represents the number of tickets Aurora sold per hour
f(x) = 0.5x - money per ticket
g(x) = 8x - tickets per hour
We replace g(x) with its value (8x).
f(g(x)) = f(8x)
We replace the x in f(x) with 8x.
f(8x) = 0,5 × 8x
f(8x) = 4x
⇒ f(g(x)) = 4x
Correct answer:
a. f(g(x)) = 4x, which represents the money Aurora made in dollars per hour
Composing functions means to use the output of the inner function as the input for the outer function.
In this case, the inner function is g(x)=8x, which means that Aurora sells 8 tickets per hour.
So, if we give 8x (number of tickets sold) as input to the function f(x)=0.5x, we'll get
[tex]f(x)=0.5x \implies f(8x)=0.5(8x)=4x[/tex]
Since the function f tells us how much Aurora gains per ticket, f(g(x)) basically means:
Aurora gains 0.5 dollars per ticket, and she sells 8 ticket per hour, so she gains 4 dollars per hour.
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A coin is tossed 10 times. The results are recording below (H=heads, T=tails). What is the experimental probability of getting heads?
H T T H H H T H T H
2/5
1/2
3/10
3/5
Answer:
3/5
Step-by-step explanation:
Out of the 10 times flipped, you got heads 6 times
That is 6/10 or 3/5
Answer:3/5
Step-by-step explanation:took the test and got right
A coin is tossed 10 times. True or false, and explain: (a) The chance of getting 10 heads in a row is 1/1,024. (b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is 1/2.
Answer:
a and b both are true.
Step-by-step explanation:
Given : A coin is tossed 10 times.
To find : True or false, and explain ?
Solution :
(a) The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex]
Coin has two face head and tail.
The probability of getting head is [tex]P(H)=\frac{1}{2}[/tex]
The probability of getting 10 heads in a row is
[tex]P=(P(H))^{10}[/tex]
[tex]P=(\frac{1}{2})^{10}[/tex]
[tex]P=\frac{1}{1024}[/tex]
The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex] is true.
(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex].
The probability of getting 10 heads in a row is [tex]P_1=(\frac{1}{2})^{10}[/tex]
The probability of getting 9 tosses were heads is [tex]P_2=(\frac{1}{2})^{9}[/tex]
Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is given by,
[tex]P=\frac{P_1}{P_2}[/tex]
[tex]P=\frac{(\frac{1}{2})^{10}}{(\frac{1}{2})^{9}}[/tex]
[tex]P=(\frac{1}{2})^{10-9}[/tex]
[tex]P=\frac{1}{2}[/tex]
Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex] is true.
(a) True: The chance of getting 10 heads in a row is [tex]\( \frac{1}{1024} \)[/tex].
(b) True: Given 9 heads, the chance of the 10th being heads remains [tex]\( \frac{1}{2} \).[/tex]
Step 1:
(a) The chance of getting 10 heads in a row:
The probability of getting heads on a single toss of a fair coin is [tex]\( \frac{1}{2} \).[/tex]
Since each toss is independent, the probability of getting 10 heads in a row is calculated by multiplying the individual probabilities:
[tex]\[ \left( \frac{1}{2} \right)^{10} = \frac{1}{1024} \][/tex]
Step 2:
(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row:
Since each toss is independent, the probability of getting heads on the 10th toss is still [tex]\( \frac{1}{2} \).[/tex]
So, the chance of getting 10 heads in a row given the first 9 were heads remains [tex]\( \frac{1}{2} \).[/tex]
Therefore, the calculations support the statements:
(a) The chance of getting 10 heads in a row is indeed [tex]\( \frac{1}{1024} \)[/tex].
(b) Given the first 9 tosses were heads, the chance of getting 10 heads in a row is still [tex]\( \frac{1}{2} \).[/tex]
Draw a line representing the "run" and a line representing the "rise" of the line. State the slope of the line in simplest form.
Answer:
-5/4
Step-by-step explanation:
See the attachment for rise and run lines. The slope is the ratio ...
slope = rise / run = -5/4
In mathematics, 'rise' and 'run' are used to find the slope of a line. They represent vertical and horizontal distances respectively between two points. Slope, represented as 'm' is calculated as 'rise/run' which gives the ratio of the vertical change to the horizontal change.
Explanation:In Mathematics, specifically in Algebra and Geometry, the terms 'rise' and 'run' refer to the vertical and horizontal distances between two points on a line, respectively. In the context of a line on a graph, the 'run' corresponds to the difference in the x-values of the points (horizontal change), while the 'rise' corresponds to the difference in the y-values of the points (vertical change). These terms are crucial when calculating the slope of a line.
The slope of a line, also often represented by the letter 'm', is computed as 'rise/run', giving us the ratio of the vertical change to the horizontal change between two points on the line. If for instance, the rise is 4 units and the run is 2 units, your slope or 'm' would be 4/2 which simplifies to 2. This means that for every step you move horizontally (run), you move two steps vertically (rise).
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