The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.
The mean of x is calculated by the following formula:
mean of x = ∑(x * P(x))
Where, ∑ = Summation operator
x = Value of random variable
P(x) = Probability of the corresponding value of x.
Let's calculate the mean of x using the formula provided above.
mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)
= -0.3 + 0 + 0.3
= 0
Therefore, the mean of x is 0.
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Angela compro un terreno rectangular que tiene un perimetro de
10x - 28a
Si el ancho del terreno es 2x - 4a
¿Cual es la expresión que muestra la medida del largo del terreno?
The expression that shows the measurement of the length of the land is L = 3x - 10a.
Let L be the length of the rectangular plot.
We know that the perimeter of a rectangle is given by the sum of the lengths of all its sides. In this case, the perimeter is 10x - 28a, so we can write:
Perimeter = 2L + 2W
10x - 28a = 2L + 2(2x - 4a)
10x - 28a = 2L + 4x - 8a
2L = 6x - 20a
L = 3x - 10a
In other words, the length of the land is equal to three times the width minus ten times the value of 'a'.
To explain this equation in a little more detail, we can say that the length of the rectangular plot is dependent on both the width of the land and the value of 'a'.
The expression tells us that as the value of 'a' increases, the length of the land decreases, and as the width of the land increases, the length of the land also increases. This equation is useful because it allows us to calculate the length of the land without having to measure it directly, as long as we know the value of 'a' and the width of the land.
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please help quickly, this needs to be finished soon
Accοrding tο the fοrmula fοr the quadratic equatiοn, the maximum height is 98 ft.
What is a quadratic equatiοn?A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn οf the fοrm:
[tex]ax^2 + bx + c = 0[/tex]
where a, b, and c are cοnstants, and x is the variable. The term "quadratic" cοmes frοm the Latin wοrd "quadratus," meaning square, because the variable is squared in this type οf equatiοn.
Quadratic equatiοns can have οne, twο, οr zerο real sοlutiοns, depending οn the values οf the cοnstants a, b, and c. The sοlutiοns can be fοund using the quadratic fοrmula:
[tex]x = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex] οr by factοring the quadratic expressiοn intο twο linear factοrs.
The quadratic functiοn tο mοdel the vertical mοtiοn is:
[tex]h(t) = -16t^2 + v0t + h0[/tex]
where:
h(t) is the height at time t
t is the time in secοnds
v0 is the initial vertical velοcity in ft/s
h0 is the initial height in ft
Given v0 = 32 ft/s and h0 = 82 ft, the functiοn becοmes:
[tex]h(t) = -16t^2 + 32t + 82[/tex]
Tο find the maximum height, we can use the vertex fοrm οf a quadratic equatiοn:
[tex]h(t) = a(t - t0)^2 + h0[/tex]
where:
a is the cοefficient οf the quadratic term
t0 is the time at which the maximum height is achieved
h0 is the initial height
Cοmparing the twο fοrms, we see that a = -16 and t0 = -b/2a, where b is the cοefficient οf the linear term. In this case, b = 32, sο:
t0 = -32 / (2(-16)) = 1
Therefοre, the maximum height is achieved at t = 1 secοnd. Substituting intο the οriginal equatiοn, we get:
[tex]h(1) = -16(1)^2 + 32(1) + 82 = 98 ft[/tex]
Sο the maximum height is 98 ft.
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What is 6/11 as a decimal rounded to 3 decimal places?
determine the dew point temperature, the humidity ratio, the specific volume and the enthalpy given a dry bulk temperature of 39oc and a wet bulb temperature of 18oc.
The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.
To determine the dew point temperature, the humidity ratio, the specific volume and the enthalpy given a dry bulk temperature of 39°C and a wet bulb temperature of 18°C, you can use a psychometric chart or a specialized software program that calculates these properties based on the given dry bulb and wet bulb temperatures, as well as other relevant parameters such as pressure, altitude, and air composition.
First, plot 39°C (the dry bulk temperature) and 18°C (the wet bulb temperature) on the chart. Then mark The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.
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Pls answer my question it will be amazing if you do just pls.
The equation to show the relationship between x and y is y = 0.08x, where y is the amount of sales tax in dollars for the item and x is the cost of the item in dollars before tax.
What is tax?Tax is a compulsory financial charge or some other type of levy imposed upon a taxpayer by a governmental organization in order to fund various public expenditures. A failure to pay, along with evasion of or resistance to taxation, is punishable by law. Taxes consist of direct or indirect taxes and may be paid in money or as its labour equivalent. Most countries have a tax system in place to pay for public, common or agreed national needs and government functions. Some levy a flat percentage rate of taxation on personal annual income, but most scale taxes based on annual income amounts.
This equation reflects the fact that the amount of sales tax for an item is 8% of its cost before tax.
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Sales tax: The equation to show the relationship between x and y is x + y = C,
What is equation?An equation is a mathematical statement that expresses two mathematical expressions to be equal. It usually consists of two numbers, variables, or a combination of the two. An equation may be used to calculate a desired result, or to determine the relationship between two variables. Equations can also be used to test whether a statement is true or false. Most equations are written in the form of "a = b," where a and b are two numbers or variables.
where C is the cost of the item plus the sales tax. This equation can be explained mathematically as follows: the cost of the item (x) is added to the amount of sales tax (y) to give the total cost of the item with tax (C).
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Find the value of x in the following diagram.
Round your answer to the nearest hundredth.
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
Find the slope-intercept form of the line with the slope m= 1/7 which passes through the point (-1, 4).
Answer:
y = 1/7x + 29/7
Step-by-step explanation:
Slope intercept form is y = mx + b
m = the slope
b = y-intercept
m = 1/7
Y-intercept is located at (0, 29/7)
So, the equation is y = 1/7x + 29/7
On January 1,1999 , the average price of gasoline was $1.19 per gallon. If the price of gasoline increased by 0.3% per month, which equation models the future cost of gasoline? y=1.19(1.003)^(x) y=1.19(x)^(1.03) y=1.19(1.03)^(x)
Answer:
first one
Step-by-step explanation:
The equation that models the future cost of gasoline is y=1.19(1.003)^(x), where "y" represents the future cost of gasoline per gallon and "x" represents the number of months since January 1, 1999.
In this equation, the initial cost of gasoline is $1.19 per gallon, and the cost increases by 0.3% per month, which is represented by the factor of (1.003)^(x).
Using this equation, you can calculate the future cost of gasoline for any number of months after January 1, 1999. For example, if you want to calculate the cost of gasoline 24 months after January 1, 1999, you can plug in x=24 and calculate y as follows:
y = 1.19(1.003)^(24)
y = 1.19(1.08357)
y = 1.288 per gallon
Therefore, the predicted cost of gasoline 24 months after January 1, 1999 is $1.288 per gallon.
Determine the total amount of money that was utilized on fuel in June 2022
Therefore, the total amount of money utilized on fuel in June 2022 is R11 095,60.
What is percent?Percent is a way of expressing a quantity as a fraction of 100. It is denoted by the symbol %, which means "per hundred". Percentages are often used to represent proportions or ratios in various fields, including finance, science, and statistics. For example, an interest rate of 5% means that for every hundred dollars borrowed or invested, five dollars of interest will be charged or earned.
Here,
(a) To calculate the total distance covered by the water tanker in March 2022, we need to find the distance travelled per day and multiply it by the number of days in March.
Distance travelled per day = 2 × 18 = 36 km (since it's a return trip)
Number of weekdays in March = 31 - 4 (Saturdays) = 27
Total distance covered = distance per day × number of weekdays
= 36 km/day × 27 days
= 972 km
(b) To determine the quantity of fuel utilized by the water tanker in March 2022, we need to divide the total distance covered by the average fuel consumption rate.
Fuel consumption rate = 5 km/ℓ
Total distance covered = 972 km
Fuel utilized = total distance covered / fuel consumption rate
= 972 km / 5 km/ℓ
= 194.4 ℓ
(c) To determine the total amount of money utilized on fuel for the water tanker in March 2022, we need to multiply the fuel quantity by the fuel price.
Fuel price in March 2022 = R16,28/ℓ
Fuel utilized = 194.4 ℓ
Total cost of fuel = fuel price × fuel quantity
= R16,28/ℓ × 194.4 ℓ
= R3 163,39
Therefore, the total amount of money utilized on fuel for the water tanker in March 2022 is R3 163,39.
(d) To determine the total amount of money utilized on fuel in June 2022, we need to repeat the above calculation using the June fuel price.
Fuel price in June 2022 = R24,14/ℓ
Fuel capacity = 460 ℓ
Total cost of fuel = fuel price × fuel capacity
= R24,14/ℓ × 460 ℓ
= R11 095,60
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Complete question:
Records of the number of water tankers that were supplied to the construction site appear in the calender on ANNEXURE A. The water source is at a distance of about 18 km (return trip) from the construction site. The water tanker has a fuel capacity of 460 litres.. The rate of fuel consumption of the Mercedes water tanker averages 5 km/ℓ. The prices of fuel per litre in March and June 2022 appear below. JUNE 2022 FUEL PRICES \begin{tabular}{|l|l|} \hline DIESEL & COST \\ \hline 50ppm & R24,14 \\ \hline \end{tabular} Source: 4.1 (a) Calculate the total distance that the water tanker has covered in March (2) 2022. (b) Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. (c) Determine the total amount of money that was utilized on fuel for the water tanker in March 2022. (2) 4.2 Determine the total amount of money that was utilized on fuel in June 2022.
Which of the following statements is about CD and CE is true? A. CD is longer than CE B. CE is longer than CD C. CD and CE are the same length D. CE is 5 units long
From the given graph, CE is longer than CD.
What is the distance between two coordinates?The length of the line segment bridging two locations in a plane is known as the distance between the points. d=√((x₂ - x₁)²+ (y₂ - y₁)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
Coordinates of E(8,6)
Coordinates of C(6,1)
Coordinates of D(3,-3)
x=8, y=6
x=6, y=1
x=3, y=-3
Distance CE=√{(8-6)² +(6-1)²} = √29
Distance CD=√{(6-3)² +(1+3)²}= √25=5
Therefore, CE is longer than CD.
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Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
X
The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.
What is surface area ?
Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.
To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.
First, let's find the area of the triangular base.
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 18 x 24
Area of triangle = 216 [tex]feet ^2[/tex]
Next, let's find the area of each rectangular face.
Area of rectangle = length x width
Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]
Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]
Area of rectangle 3 = 22 x 30 = 660 [tex]feet ^2[/tex]
Now, we can add up the areas of all three faces to get the total surface area of the prism:
Surface area = area of rectangle (1+2+3) + 2 x area of triangle
Surface area = 528 + 396 + 660 + 2(216)
Surface area = 2016 [tex]feet ^2[/tex]
Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].
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three traffic lights on a street span 120 yards. if the second traffic light is 85 yards away from the first, how far in yards is the third traffic light from the seccond
The distance between the third traffic light from the second traffic light is 35 yards.
What is the distance?Three traffic lights on a street span 120 yards.
If the second traffic light is 85 yards away from the first.
Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.
This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.
Thus, the distance between the third traffic light from the second traffic light is 35 yards.
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Which expression represents the perimeter of a triangle in simplest form that has side lengths: 2x, 3x + 5, x + 2
Answer:
6x + 7
Step-by-step explanation:
triangle has 3 sides right, which is 2x, 3x+5 and x+2
so basically you just have to add everything up since perimeter is just the total number of each sides combined
2x + (3x+5) + (x+2)
expand from the brackets
2x + 3x + 5 + x + 2
rearrange the numbers to avoid confusion
2x + 3x + x + 5 + 2
add everything up
6x + 7
Solve for x,
using the tangent lines.
X
42°
x = [?]
can someone pls help explain how they got the answer? i’m having a hard time understanding, ty :)
Answer:
138°
Step-by-step explanation:
You want the measure of the angle at two tangents when they intercept an arc of 42°.
Supplementary anglesThe short answer is that the exterior angle x is the supplement of the measure of the arc:
x = 180° -42°
x = 138°
Exterior angleAn exterior angle where secants meet is half the difference of the arcs of the circle they intercept. Here, the secants have been located so the corresponding chord length between the near and far circle intercept points have degenerated to zero. That is, they are tangents.
The angle relation still holds:
x = (long arc - short arc)/2 = ((360° -42°) -42°)/2 = (360° -2·42°)/2
x = 180° -42° = 138°
QuadrilateralThe tangents, together with their associated radii form a quadrilateral. The angles at the tangents are 90°, and the total of all angles is 360°. This gives us the relation ...
x + 90° +42° +90° = 360°
x +42° = 180° . . . . . . . . . . . . . subtract 180°
x = 180° -42° = 138°
(We solved this with an extra step, so you could see the same "supplementary angles" relationship between x and 42°.)
A and B are independent.
If P(A) = 1/2 and P(An B) = 6/15
The tape diagram represents an equation.
Write an equation to represent the image.
Answer: y+y=7
Step-by-step explanation:
7 is as big as 2 y's therefore y+y would be equal to 7
given the results of the two hypothesis tests, would you reject or fail to reject your null hypotheses (assuming a 0.05 significance level)? what does your decision mean in the context of this problem? would you proceed with changing the design of the shopping cart icon, or would you stay with the original design?
Assuming a 0.05 significance level, both hypothesis tests would reject the null hypothesis. This means that there is enough evidence to suggest that the shopping cart icon's design affects the users' behavior. Therefore, the design should be changed to improve the user's experience.
Step by step explanation:
The problem is not stated, so we need to make some assumptions. We will assume that the hypothesis tests were done to determine whether a change in the shopping cart icon design would affect the users' behavior.
The null hypothesis (H0) is that the design of the shopping cart icon does not affect the users' behavior, while the alternative hypothesis (Ha) is that the design of the shopping cart icon affects the users' behavior.
The significance level is 0.05, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).
If both hypothesis tests reject the null hypothesis, it means that the p-values were less than 0.05, and there is enough evidence to suggest that the design of the shopping cart icon affects the users' behavior.
Therefore, it is recommended to proceed with changing the design of the shopping cart icon to improve the user's experience.
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Austin has a dimes and y nickels, having at most 28 coins worth a minimum of $2
combined. At least 18 of the coins are dimes and no more than 6 of the coins are
nickels. Solve this system of inequalities graphically and determine one possible
solution.
The solution of system of inequalities solved graphically is (18,6).
What is system of linear inequalities?A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.
Let us suppose the number of dimes = a.
Let us suppose the number of nickels = y.
According to the problem we have the following conditions:
a + y ≤ 28 (at most 28 coins)
0.10a + 0.05y ≥ 2 (worth at least $2)
a ≥ 18 (at least 18 dimes)
y ≤ 6 (no more than 6 nickels)
Using different values of a and y plot the points.
The solution of this system of inequality is any point that lies in the feasible region.
One such point is (18, 6).
Hence, the solution of system of inequalities solved graphically is (18,6).
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a study was conducted on students from a particular high school over the last 8 years. the following information was found regarding standardized tests used for college admitance. scores on the sat test are normally distributed with a mean of 990 and a standard deviation of 201. scores on the act test are normally distributed with a mean of 21.6 and a standard deviation of 4.1. it is assumed that the two tests measure the same aptitude, but use different scales.If a student gets an SAT score that is the 70-percentile, find the actual SAT score. SAT score = _____ Round answer to a whole number. What would be the equivalent ACT score for this student? ACT score = ____Round answer to 1 decimal place.If a student gets an SAT score of 1536, find the equivalent ACT score. ACT score = ____ Round answer to 1 decimal place.
We are given that the SAT and ACT measure the same aptitude but use different scales. To find the equivalent ACT score for a given SAT score, we can use the conversion chart.
SAT 1100 = ACT 23
Therefore, the equivalent ACT score for a student with an SAT score of 1104 is 23.
3. If a student gets an SAT score of 1536, find the equivalent ACT score.
Solution:
To find the equivalent ACT score for a given SAT score, we can use the conversion chart.
SAT 1536 = ACT 35
Therefore, the equivalent ACT score for a student with an SAT score of 1536 is 35.
Therefore, the SAT score = 1536 and the ACT score = 35.
1. If a student gets an SAT score that is the 70th percentile, find the actual SAT score.
Solution:
We are given that SAT scores are normally distributed with a mean of 990 and a standard deviation of 201. We are asked to find the SAT score for the 70th percentile.
P( SAT score < X) = 0.70
We can use the standard normal table to find the corresponding z-score for the 70th percentile.
z = 0.52
We can use the z-score formula to find the SAT score:
z = (X - μ) / σ
0.52 = (X - 990) / 201
X = 1103.72
Therefore, the actual SAT score for the 70th percentile is 1104.
2. What would be the equivalent ACT score for this student?
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A grocer has two kinds of candies, one selling for 90 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
? pounds of 40 − cent candies, ? pounds of candies that cost $1.40 per pound
Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
So, we have:
x + y = 100 .........A
40 × x + 140 y = 85 × 100
40 x + 140 y = 8500 ........B
Solving (A) and (B) as follows:
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
0 + 100 y = 4500
y = 4500/100
Hence, the price per unit of grocery is $1.40 = y = 45 pounds.
Now, put the value of y in equation (A) as follows:
x + y = 100
x = 100 - y
x = 100 - 45
x = 55 pounds
The number of groceries at the 40-cent price is x = 55 pounds.
Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
the ratio of students who ade the honor roll to the total number of stoudents is 1:50. if there are 500 students in total how many made the honor roll?
If there are 500 students in total, the number of students who made the honor roll is 10 students, given that the ratio of students who made the honor roll to the total number of students is 1:50.
The number of students who made the honor roll can be found using proportions. Here's how to do it:
Let X be the number of students who made the honor roll.
The proportion can be set up using the given ratio as follows:
1:50 = X:500
Cross-multiplying this equation and solving for X gives:
50X = 500
X = 10
Therefore, 10 students made the honor roll.
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4-77 Is the relationship shown in the 28+
graph at right below proportional? If
241
so, find the unit rate. If not, explain
why not.
The graph is/is not proportional
because
Unit rate:
Cost ($)
20
16-
12+
8
2 3 4 5
Number of Books
Purchased
Answer:
Step-by-step explanation:
A graph is proportional if the relationship between the two variables represented on the axes is constant, meaning that if one variable increases, the other variable also increases by the same factor. In other words, the graph forms a straight line that passes through the origin.
To find the unit rate, you need to look for the constant of proportionality, which is the ratio between the two variables represented on the graph. In this case, the variables are the number of books purchased and the cost in dollars.
If the graph is proportional, then the unit rate is the constant of proportionality, which is the cost per book. You can find the unit rate by dividing the total cost by the number of books purchased. For example, if the total cost for 4 books is $16, then the unit rate would be $4 per book.
If the graph is not proportional, then there is no constant of proportionality, and the unit rate cannot be calculated. The relationship between the two variables may be nonlinear, meaning that the rate of change between the variables is not constant.
The ratio of distance runners to sprinters on a track is 5:3 how many distance runners and sprinters could be on the track team
Runners and sprinters could be on the track team is 25 distance.
Distance:
Distance is a qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria (such as "more than two counties"). The term Distance is also often used metaphorically to refer to a measure of the amount of difference between two similar objects.
According too the Question:
Based on the based Information:
15× 5÷3
canceling all the common factor, we get:
5 × 5 = 25
Now, the Product or Quotient is 25.
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A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)
(a) n = 10, p = 1/4, and x = 5. Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)
(b) P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)
Here n = 10, p = 1/4, and x = 5.Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)
Find P(More than 3)For this, we need to calculate P(4), P(5), P(6),...,P(10) and add them.Using the formula of binomial probability function,P(4) = 10C4 * (1/4)^4 * (3/4)^6 = 0.2503 (rounded to three decimal places)P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)P(6) = 10C6 * (1/4)^6 * (3/4)^4≈ 0.0014 (rounded to three decimal places)P(7) = 10C7 * (1/4)^7 * (3/4)^3≈ 0.0001 (rounded to three decimal places)P(8) = 10C8 * (1/4)^8 * (3/4)^2≈ 0.0000 (rounded to three decimal places)P(9) = 10C9 * (1/4)^9 * (3/4)^1≈ 0.0000 (rounded to three decimal places)P(10) = 10C10 * (1/4)^10 * (3/4)^0≈ 0.0000 (rounded to three decimal places)P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)
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[amc10b.2011.7] the sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is $30^{\circ}$ larger than the other. what is the degree measure of the largest angle in the triangle?
The degree measure of the largest angle is 72° in the triangle.
We have, The sum of two angles of a triangle is 6/5 of a right angle.
One of these two angles is 30° larger than the other.
Let A and B be the two angles of the triangle such that A = B + 30°.
We know that the sum of three angles in a triangle is 180°.
⇒ A + B + C = 180°
⇒ B + 30° + B + C = 180°
⇒ 2B + C = 150°
We also know that the sum of two angles of a triangle is 6/5 of a right angle.
⇒ A + B = 6/5 × 90°
⇒ B + 30° + B = 108°
⇒ 2B = 78°
⇒ B = 39°
C = 150° - 2B ⇒ 72°
A = B + 30° ⇒ 39° + 30° ⇒ 69°
Therefore, the degree measure of the largest angle in the triangle is 72°.
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At the bookstore, best-sellers are normally $19.95 each. During the store-wide 20% off sale, how much would it cost you, before tax, to buy two best-sellers?
F. $3.99
G. $7.98
H. $15 96
J. $31.92
K. $39.90
Step-by-step explanation:
20% off means you pay 80 % of the original price for two books
80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92
ramona owns a small coffee shop, where she works full-time. her total revenue last year was $200,000, and her rent was $5,000 per month. she pays her one employee $3,000 per month, and the cost of ingredients averages $1,000 per month. ramona could earn $55,000 per year as the manager of a competing coffee shop nearby. her economic profit last year was were....
a. $18,000
b. $37,000
c. $55,000
d. $66,000
e. $92,000
Ramona's economic profit last year was $92,000 - $55,000 = $37,000. Therefore, the correct option is b. $37,000.
Ramona owns a small coffee shop, where she works full-time. Her total revenue last year was $200,000, and her rent was $5,000 per month. She pays her one employee $3,000 per month, and the cost of ingredients averages $1,000 per month. Ramona could earn $55,000 per year as the manager of a competing coffee shop nearby. Her economic profit last year was $37,000.An economic profit can be calculated by subtracting total costs from total revenue. Given that Ramona's total revenue is $200,000, her total cost is $5,000 + $3,000 + $1,000 = $9,000 per month. Multiplying this by 12 gives us her total cost for the year: $9,000 x 12 = $108,000. Ramona's economic profit last year was therefore $200,000 - $108,000 = $92,000. However, this figure doesn't take into account the opportunity cost of Ramona earning $55,000 as the manager of a competing coffee shop nearby. This needs to be subtracted from Ramona's economic profit.
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a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:
The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.
What is the z-score?The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.
z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.
z = {x-μ}/{σ} = {-20-0}/{8} = −2.5
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.
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HELP ASAP!!
A kite is flying 10 feet off the ground. It’s line is pulled out in casts a 9 foot shadow, find the length of the line if necessary round to the nearest 10th.
Answer:
We can use similar triangles to solve this problem. Let's call the length of the kite's line "x". Then, we can set up a proportion:
(length of kite) / (length of shadow) = (height of kite) / (length of shadow)
x / 9 = 10 / 9
To solve for x, we can cross-multiply and simplify:
x = 90 / 9
x = 10
Therefore, the length of the kite's line is 10 feet.
Step-by-step explanation:
