Answer: The tip is $14.00
Step-by-step explanation: 20% of 70 is 14.
Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X.
X 0 1 2 3 4 or more
probability 0. 58 0. 23 0. 11 0. 05 0. 03
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F.
(a) Construct the probability distribution of the random variable Y.
(b) Determine the mean and standard deviation of Y. Show your work.
Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0. 40 and 0. 66, respectively. The fat quarters sell for $5. 00 each but are discounted by $1. 50 for each defect found.
(c) What are the mean and standard deviation of the selling price for the fat quarters sold by Company G?
The probability distribution of the random variable Y is 0.63, 0.25, 0.12. The mean of y is 0.4899 and the std deviation of y is 0.6999 and the mean of the selling price for the fat quarters sold by Company G is $4.4 and the std deviation for the same is $0.99
a) x = number of defects on a fat quarter
to be sold, X must be, X ≤ 2
y = number of defects on the sellable fat quarter,
now from the table, P [fat quarter being sellable]
=P [X ≤ 2]
=0.58 + 0.23 + 0.11
= 0.92
Therefore, P[y-0] = P[x=0Ix≤2]
=[tex]\frac{P[x=0][x < 2]}{P[x < 2]}[/tex]
=P[y=0] = 0.63
P[y=1] = P[x=1Ix≤2]
P[y=1] = [tex]\frac{0.23}{0.92}[/tex]
=0.25
P[y=2] = P[x=2Ix≤2]
P[y=2] = [tex]\frac{0.11}{0.92}[/tex]
= 0.12
y------------------0--------1---------2
probability---0.63----0.25----0.12
b)mean of y = E(y)
=0²×0.063+1×0.25+2×0.12
=0.25+0.24
=0.49
now we know that E(y²) = 0²×0.63+1²×0.25+2²×0.12
=0.25+0.48
=0.73
E(y²) - [E(y)]²
=0.73-0.49²
=0.4899
std deviation of y = 0.6999
c) now that we have E(G) = 0.40, √v(G) = 0.66
let s be selling price of fat quarters, then s = 5.00 - 1.50 × (G)
therefore = 5-1.5×0.4
=5-0.6
=$4.4 is the mean selling price.
now for the standard deviation price = v[5-1.5G]
=v(5)+1.5² v(G)
=0+2.25×0.66²
=v(s)= 0.9801
standard deviation of sp =√v(s)
=$0.99
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Today a typical family of four spends $897. 20/ month for food. If inflation occurs at the rate of 4%/ year over the next 9 years, how much should the typical family of four expect to spend for food 9 years from now?
In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.
In order to determine how much a normal family of four should budget for food in 9 years, we must take inflation into consideration.
To account for inflation, we can use the formula below to determine the future worth of the current food expenditures:
Future value = Present value * (1 + inflation rate)^n
where:
Present value = $897.20/month
Inflation rate = 4% per year
n = number of years
When we substitute the specified values, we get:
Future value = $897.20 * [tex](1 + 0.04)^9[/tex]
= $897.20 * 1.3981
= $1254.77 (to two decimal places in rounding)
Therefore, In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.
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what's the rate of change of -7≤x≤-2
Answer:
4
Step-by-step explanation:
Rate of change forumla
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
We have our X points, -7 and -2. Now to find the Y value at those places.
For -7, Y is 5
For -2, Y is 25
Now we plug this into the equation
[tex] = \frac{25 - 5}{ - 2 - ( - 7)} = \frac{20}{5} = 4[/tex]
which expressions will have a positive answer? assume all variables represent numbers larger than zero (select all that apply)
Answer:
bro do u have a pic i will give u your points back but i need a pic to help
Step-by-step explanation:
What is the area of this figure?
The area of the figure is given as follows:
100.56 mm².
How to obtain the area of the figure?The figure in this problem is composed as follows:
Rectangle of dimensions 4 mm and 12 mm.Rectangle of dimensions 2 mm and 7 mm.Rectangle of dimensions 4 mm and 12 - 7 = 5 mm.Rectangle of dimensions 3 mm and 2 mm.Semicircle of radius 2 mm.The areas for each region are given as follows:
Rectangle of dimensions 4 mm and 12 mm -> 4 x 12 = 48 mm²Rectangle of dimensions 2 mm and 7 mm -> 2 x 7 = 14 mm².Rectangle of dimensions 4 mm and 12 - 7 = 5 mm -> 4 x 5 = 20 mm².Rectangle of dimensions 3 mm and 2 mm -> 3 x 2 = 6 mm².Semicircle of radius 2 mm -> 3.14 x 2² = 12.56 mm².Hence the total area is of:
48 + 14 + 20 + 6 + 12.56 = 100.56 mm².
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There are 250 people in a museum
2/5 of the 50 peoples are girls
3/10 of the 50 people are boys
The rest of the 250 people are adults
Work out the number of adults in museum
The number of adults in the museum, using the fractional value of girls and boys, is 75.
What is a fractional value?A fractional value refers to a portion of the total value.
A fractional value can be depicted in fractions, decimals, or percentages.
A fractional value can also be represented as a ratio or proportion.
In this situation, the fractional number of adults is determined using subtraction.
The total number of people in a museum = 250
The fraction of girls in the museum = 2/5
2/5 of 250 = 100 girls
The fraction of boys in the museum = 3/10
3/10 of 250 = 75
Alternatively:
2/5 + 3/10 = 7/10
7/10 of 250 = 175
Therefore, the number of adults = 75 [250 - (100 + 75)]
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Complete Question:There are 250 people in the museum.
2/5 of the 250 people are girls.
3/10 out of the 250 people are boys.
The rest of the 250 people are adults.
Work out the number of adults in the museum.
there are 30 people in a classroom. ignoring the potential of a leap-year birthday (so 365 days), what is the probability that at least one pair of people have the same birthday?
The probability that at least one pair of people have the same birthday, with 30 people in a classroom is approximately 0.7063.
To solve this problem, we can use the concept of the complement of an event. The complement of the event "at least one pair of people have the same birthday" is the event "no pair of people have the same birthday." So, we can find the probability of this complement event and subtract it from 1 to get the probability of the original event.
The probability that the first person has a unique birthday is 1, since there are no other people in the room yet. The probability that the second person also has a unique birthday is (364/365), since there are 364 remaining days in the year that they could be born on.
Similarly, the probability that the third person has a unique birthday is (363/365), and so on, down to the 30th person, whose probability of having a unique birthday is (336/365).
To find the probability that no pair of people have the same birthday, we can multiply these probabilities together:
P(no pair share a birthday) = 1 * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937
Therefore, the probability that at least one pair of people have the same birthday is:
P(at least one pair share a birthday) = 1 - P(no pair share a birthday) ≈ 1 - 0.2937 = 0.7063
So the probability that at least one pair of people have the same birthday is approximately 0.7063, which is quite high. This is known as the birthday problem or birthday paradox.
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if a t test yields p > 0.05 the null hypothesis would normally be: select one: a. accepted. b. rejected. c. accepted under certain conditions. d. there is not enough information for you to evaluate the findings.
if a t test yields p > 0.05 the null hypothesis would normally be option (A) accepted
The null hypothesis defined as the types of hypothesis that do not have any statistical significance exist in the given set of observation.
The p value is defined as the measurement that is used to validate the hypothesis using the observed data. The range of the p value varies from zero to one. Zero means no chance and 1 means absolute certainty
If a t test yields a p-value greater than 0.05, it means that there is insufficient evidence to reject the null hypothesis, and the results are not statistically significant. Therefore, the null hypothesis is accepted.
Therefore, the correct option is (A) accepted
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In the figure below, find mzABC.
B
D
m/ABC=
The measure of angle ABC from the given circle D is 34°.
What is angles in the same segment theorem?The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.
Given that, circle with the center D and measure of arc AC is 34°.
The measure of arc = m∠ABC
m∠ABC =34°
Therefore, the measure of m∠ABC is 34°.
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Rewrite 26/9 as a mixed number. help me
The required mixed number of 26/9 is given as 2 8/9.
What is a mixed number?A mixed number is a number that consists of a whole number and a proper fraction. It is written in the form "a b/c", where "a" is the whole number, "b" is the numerator of the proper fraction, and "c" is the denominator of the proper fraction.
Here,
To rewrite 26/9 as a mixed number, we need to divide the numerator (26) by the denominator (9) and express the result as a whole number and a proper fraction.
26 ÷ 9 = 2 with a remainder of 8
The whole number part is 2, and the proper fraction part is 8/9, since 8 is the remainder and 9 is the denominator.
Therefore, 26/9 as a mixed number is 2 8/9.
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What is the value of F?
You are building a ramp that must cover a horizontal distance of
exactly 13 feet. The angle of the ramp from the ground is 8°.
Determine the length of the ramp, in feet. Round to two decimal
places as needed.
The length of the ramp that must cover the horizontal distance is 13.13 feet.
What is the length of the ramp, in feet ?Given the data in the question, this forms a right-triangle.
Angle θ = 8°Adjacent of angle θ = 13ftLength of the ramp = hypotenuse = ?To solve for the length of the ramp, we use trigonometric ratio
Cosine = Adjacent / Hypotenuse
Plug in the values
cos( 8° ) = 13ft / hypotenuse
Hypotenuse = 13ft / cos( 8° )
Hypotenuse = 13.13 ft
Therefore, the ramp's length is 13.13 ft.
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A football coach is trying to decide what team is ahead lay in the girl with strategies better play the regular Defense play a prevent DFS the guards or against lol games, but make sure Gaines easier the coach of use the outcome of 100 games
The greater probability is the probability of winning through the use of regular defense.
How to solve for the probabilityIf out of the 100 games that were reviewed, the defense games were 50 and the prevent defense games were 50 as well
Out of the regular 50, there are 38 wins and then 12 loses. Out of the prevent games, there 29 wins and 21 loses.
The probability to win by regular is 38 / 50 = 0.76
the probability to win by prevent defense is 29 / 50 = 0.58
0.76 is greater than 0.58 hence the decision would be to win the game by playing the regular defense.
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A football coach is trying to decide: When a team is ahead late in the game, which strategy is better?
Play the "regular" defense.
Play a "prevent" defense that guards against long gains but makes short gains easier.
The coach reviews the outcomes of 100 games.
Compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. Draw a conclusion based on your results.
Select the correct answer.
If f(x) = 3x+2 and g(x) = 2x - 2. what is (f- g)(x)?
OA. X+4
OB. X-2
OC. X
OD. 5x-2
O E.
X-4
Answer:
A
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1
= 3x + 2 - 2x + 2 ← collect like terms
= x + 4
A system of equations is shown.
y=x+1
x-2y=-4
Which represents the solution of this system?
O(-2, -3)
O(-2, 3)
(2, -3)
(2, 3)
Look at the expression and fill in the correct number in each blank.
The given expression has
term(s) with
1,500(1+1)*
factors.
The expression has 3 terms and 3 factors
What are the terms of the equationThe terms are the constant, the r term and the t term
The factors that are in the equation are 1500, 1 and 12
What is an exponential equation?An exponential equation is an equation that involves an exponential function, which has the form f(x) = a^x, where "a" is a constant base and "x" is the exponent. Exponential equations are used to model phenomena that grow or decay at a constant relative rate. The solutions to exponential equations can be found by manipulating the equation algebraically to isolate the variable in the exponent, taking logarithms of both sides, or by using exponential rules such as the power rule or the product rule.
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The blood platelet count of a group of women have bell-shaped distribution with a mean of 245.5 and a standard deviation of 68.2 (all units are 1000 cells/ L) Using the empirical rule, fill in the blanks below (Round to the nearest hundredth):
a. Approximately 95% of healthy women in this group
b. Approximately 99.7% of healthy women in this have blood platelet counts between
group have blood platelet counts between
and(1000 cells/ ML). and (1000 cells/ ML).
The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8
The given parameters are:
μ = 248.5
[tex]\sigma = 61.1\\[/tex]
(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7
Start by calculating the z-score, when x = 126.3 and x = 370.7
[tex]Z = \frac{(x-u)}{\sigma}[/tex]
So, we have:
x = -2
Also,
x = 2
The empirical rule states that:
Approximately 95% of the data lies within 2 standard deviations of the mean.
Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.
(b) The percentage with platelet count between 65.2 and 431.8
Start by calculating the z-score, when x = 65.2 and x = 431.8
So, we have:
Z =-3
Also:
Z = 3
The empirical rule states that:
Approximately 99.7% of the data lies within 3 standard deviations of the mean.
Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8
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Solve the word problem below. Enter your answer in simplest terms, using the
slash (/) to represent the fraction bar.
You have 4/6 cup of oatmeal in your cupboard. A recipe for cookies calls for 1/4
cup of oatmeal. How much oatmeal would you have left if you made the
cookies
Answer:
5/12
Step-by-step explanation:
4/6 - 1/4 The common denominator would be 12
8/12 - 3/12 = 5/12
Answer:
5/12
Step-by-step explanation:
mark me please
If the scale factor of figure A to figure B is 3:8 find the value of x
If the scale factor of figure A to figure B is 3:8, the value of x is 9.
We are given Figure A and Figure B, along with their respective scale factors. To solve the problem, we must utilize the proportion rule. The ratio of the two figures is 3:8, so we can write the equation for proportion as follows -
3/8 = x/24
Applying the cross-multiplication rule, we get,
3 * 24 = 8 * x
Further solving for the value of x, we get,
x = (3 * 24) / 8
x = 9
Hence, the value of x is 9.
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The complete question is -
If the scale factor of figure A to figure B is 3:8 find the value of x.
PQRS is a trapezium, and AB ∥ PS ∥QR. If PA = 3 cm, AQ = 1.4 cm, BR = 2.1 cm,
then SB =
Answer:
In trapezium PQRS, AB is parallel to PS and PS is parallel to QR. Since we know the lengths of PA, AQ, and BR, we can calculate the length of SB as follows:
SB = PA + BR - AQ = 3 + 2.1 - 1.4 = 3.7 cm
Someone quick help me with this please?
Answer:
Not equal and Congruent should be your answers
Pls show your work thank you will mark the Brainliest
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
According to graph, the value of p(x) = 8, when x = -2, as this point lies on the curve ~
Now, put the value of x in each of the choices provided to check if its equal to 8.
[tex]\qquad \sf \dashrightarrow \: p( x) = (0.35) {}^{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = (0.35) {}^{ - 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = \dfrac{1}{(0.35 ){}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = \dfrac{1}{0.1225} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = 8.1632[/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) \approx 8[/tex]
Since the value satisfy the first equation, the correct choice will be (A)
Sarah charges $12 an hour when she
babysits. She also charges a non-refundabl
$5 fee just for showing up. What equation
could be used to represent the relationship
between x, the number of hours she
babysits, and y, the amount of money she
makes? jo
The equation which correctly shows the relationship between x, number of hours and y, the amount of money she makes is; y = 12x + 7.
What is the relationship between x and y as described?It follows from the task content that the relationship between y and x is to be.
By comparison with the slope-intercept equation; y = mx + c.
Since, slope, m is the rate of change; m = 12$ per hour.
Also, the nonrefundable one-time fee for showing up represents the y-intercept, c.
Therefore, the required equation is;
y = 12x + 5.
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Find a vector equation and parametric equations for the line segment that joins P to Q.
P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )
vector equation r(t)
parametric equations x(t), y(t), z(t)
The vector equation for a line segment that joins two points P and Q can be found by subtracting the position vectors of P and Q and representing the result as a vector from P.
The position vector of point P is given by [0, -4, 4] and the position vector of point Q is given by [1/2, 1/3, 1/4]. So, the direction vector of the line segment is found by subtracting the position vectors:
d = Q - P = [1/2, 1/3, 1/4] - [0, -4, 4] = [1/2, 5/3, -3/4]
The vector equation of the line segment can be written as:
r(t) = P + t * d = [0, -4, 4] + t * [1/2, 5/3, -3/4] = [t/2, -4 + 5t/3, 4 - 3t/4]
where t is a scalar parameter that varies from 0 to 1 to give the points on the line segment between P and Q.
The parametric equations of the line segment are:
x(t) = t/2
y(t) = -4 + 5t/3
z(t) = 4 - 3t/4
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Find a vector equation and parametric equations for the line segment that joins P to Q?
P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )
vector equation r(t)
parametric equations x(t), y(t), z(t)
What is the graph of the following function? Click on the graph until the correct one appears.
g(x) = {<1}X-2, X21-4x+3, x < 1
Pls i need help !!!
The graph of the piecewise function is given by the image presented at the end of the answer.
How to graph the piecewise function?A piecewise function is a function that has multiple definitions, according to it's input values.
The two definitions for this problem are given as follows:
Until x = 1.Right of x = 1.For the values until x = 1, we have an increasing linear function, with intercept of y = -2, and finishes at the point (1,-1).
For the values greater than x = 1, the function is a linear function, starting at the point (1,-1), and decaying.
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anyone knows the answer for this?
The blank in the statement should be filled in with "ΔVYZ." which is proven by the definition of congruence.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.
Since S, T, and U are midpoints in ΔVYZ, it follows that:
ST is a median of ΔVYZ, meaning it bisects the side VZ into two equal parts.
TU is a median of ΔVYZ, meaning it bisects the side VY into two equal parts.
SV is a median of ΔVYZ, meaning it bisects the side YZ into two equal parts.
Using the definition of congruence, two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure. Since medians bisect their corresponding sides, it follows that all three pairs of corresponding sides in ΔYST, ΔTUZ, and ΔSVU are equal in length.
Furthermore, since the medians divide the triangle into two smaller triangles that are similar to the original triangle, it follows that the corresponding angles in ΔYST, ΔTUZ, and ΔSVU are equal in measure.
Therefore, ΔYST ≅ ΔTUZ ≅ ΔSVU ≅ ΔVYZ.
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Help please it´s urgent
Based on this graph, what is the solution to the system of equations?
Answers:
A. There are an infinite number of solutions.
B. There is no solution.
C. (1, 3)
D. (2, 3)
E. (3, 2)
Answer: E
Step-by-step explanation:
The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.
What is the area of this compound figure? PLEASE HELP
The area of the composite figure is equal to 254 m² square metres.
How to calculate for the area of the figureThe composite figure can be observed to be a vertical rectangle, a square and an horizontal rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:
area of the vertical rectangle = 19 m × 7 m
area of the vertical rectangle = 133 m²
area of the square = 5 m × 5 m
area of the square = 25 m²
area of the horizontal rectangle = 16 m × 6 m
area of the horizontal rectangle = 96 m²
total area of the composite figure = 133 m² + 25 m² + 96 m²
total area of the composite figure = 254 m²
Therefore, the area of the composite figure is equal to 254 m² square metres.
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What is the percent of change from 90 to 18?
* 80% increase
*80% decrease
*75% decrease
*75% increase
*25% increase
The percent of change is the change in value in percent from 90 to 18 that is an 80% decrease.
To calculate the percent change from 90 to 18, we first need to find the difference between the two values:
Change = Final Value - Initial Value
Change = 18 - 90
Change = -72
The negative sign indicates that there has been a decrease in value.
To find the percent change, we can use the following formula:
Percent Change = (Change / Initial Value) x 100%
Percent Change = (-72 / 90) x 100%
Percent Change = -80%
So there is decrease in percent from 90 to 18 that is by 80%.
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we need to survey a random sample of the 300 passengers on a flight from san francisco to tokyo. you randomly select a seat position (right window, right center, right aisle, etc.) and survey all the passengers sitting in those seats. what sampling technique best describes the process here?
The sampling technique best described here is systematic sampling. Systematic sampling is a type of probability sampling in which the elements in the population are selected in a systematic way
This sampling technique is used when the population size is too large to survey the entire population. In this example, the population size is 300 passengers and the sampling interval is determined by dividing the population size by the sample size. For example, if the sample size is 30, the sampling interval is[tex]10 (300/30=10).[/tex] This means that every 10th passenger is randomly selected for the survey. The selection starts with a randomly chosen passenger and then the ninth passenger after that is selected and so on. The formula for Systematic sampling is n = N/n, where N is the population size and n is the sample size.
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