Answer:1st one
Step-by-step explanation:
An arch of a bridge is made up by bending a steel beam into the shape of a semi circle 20m
the length of the steel beam is approximately 31.4 meters to the nearest meter.
The length of the steel beam is equal to the circumference of the semi-circle formed by bending the beam into the shape of an arch.
The formula for the circumference of a circle is:
C = πd
Where C is the circumference, π is the value of pi, and d is the diameter of the circle.
Since the arch is a semi-circle, the diameter is equal to the span of the arch, which is 20m. So we can calculate the circumference of the arch as follows:
C = πd/2
= 3.14 x 20m / 2
= 31.4m
Therefore, The steel beam measures, to the nearest meter, 31.4 meters in length.
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Complete Question
An arch of a bridge is made by bending a steel beam into the shape of a semi circle, if the span (diameter) of the arch in 20m, use the value 3.14 for pi to find the length of the steel beam to the nearest meter.
What is the Area and Volume of this prism?
The area of the prism is given by the sum of the areas of all the parts that compose the prism.
The parts that compose the prism are given as follows:
Rectangular base of dimensions 3m and 5m.Rectangle of dimensions 5m and 10 m.Two right triangles of sides 3m and 10 m.Hence the area of the prism is given as follows:
A = 3 x 5 + 5 x 10 + 2 x 1/2 x 3 x 10
A = 95 m².
The volume is given by the multiplication of the base area by the height, hence:
Base area = 5 x 3 = 15 m².Height of 10 m.Thus:
V = 15 x 10 = 150 m³.
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auditors compared opinions about treatment (very good/acceptable/poor) at four va hospitals (labeled a,b,c,d) among veterans aged 50 and above. what are the hypotheses for a chi-square test of independence on the data? select one:
The hypotheses for a chi-square test of independence on the data that auditors compared opinions about treatment (very good/acceptable/poor) at four VA hospitals (labeled a,b,c,d) among veterans aged 50 and above are:
Null hypothesis, H0: There is no association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Alternative hypothesis, Ha: There is an association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.
An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.
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What is the value of v i need help
Therefore , the solution of the given problem of unitary method comes out to be V has a value of -13/3.
What is a unitary method?By using preexisting variables, this common convenience, or all essential components from the initial Bishop malleable study that adhered to a specific methodology, the objective may be accomplished. If the term affirmation result does not occur, both essential components will event miss the statement; however, if it does, it then becomes possible to reach the entity once more.
Here,
TU = 4v and QR = 5v plus 17 allow us to write:
=> QR = TU + UP + PS + SR + RQ
Inputting the numbers provided yields:
=> 5v + 17 = 4v + UP + v + 26 + SR + 5v plus
When we simplify the solution, we obtain:
=> UP + SR + 6v + 26 = 0
Because UP and SR are opposite and equivalent, we can write:
=> UP = -SR
By replacing this in the preceding solution, we obtain:
=> UP - UP + 6v + 26 = 0
When we simplify the solution, we obtain:
=> 6v + 26 = 0
26 is subtracted from both parts to yield:
=> 6v = -26
When we multiply both parts by 6, we get:
=> v = -26/6
If we simplify, we get:
=> v = -13/3
V therefore has a value of -13/3.
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you roll two six-sided dice at the same time. what is the probability the second dice landed on an even number given the first one landed on an odd number?
The probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
Step-by-Step Explanation:Let A be the event that the first dice rolls an odd number, and let B be the event that the second dice rolls an even number. We want to find P(B|A), which is the probability of B given A. This can be found using the formula:P(B|A) = P(A and B) / P(A) We know that P(A) = 1/2, as half the numbers on a six-sided dice are odd.
To find P(A and B), we need to find the probability that both dice roll the desired numbers simultaneously. Since we know that the first dice rolled an odd number, only half of the numbers are possible for the second dice to be even. Therefore, P(A and B) = 1/2 x 1/2 = 1/4. So:P(B|A) = P(A and B) / P(A) = (1/4) / (1/2) = 1/2 or 0.5. Therefore, the probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.
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please answer i have 5 minutes i need an answer FAST!!!
(8.15x4 divided by 5) x 3.2 = _____.
Answer:
20.864
Step-by-step explanation:
8.15 x 4 is 32.6. I used a calculator but what I would do if I were solving on paper would be to double it, and then double it again.
Then, we divide 32.6 by five to get 6.52. I did this with a calculator, but if I were solving on paper, I would divide by 10 (move decimal point), and then double it.
Finally, we muliply 6.52 by 3.2. I did this with a calculator and got 20.864, but if I was doing this on paper, I would just solve using standard form!
Let me know if this helped by hitting brainliest! If you have any questions, comment and I'll get back to you ASAP.
What is the the circumference of the circle with a 16 radius? (in terms of pi)
The circumference of the circle with a radius of 16 is 32π using formula for the circumference of a circle is C = 2πr.
The circumference of a circle is the distance around the perimeter of the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is the constant pi, and r is the radius of the circle.
In this case, the radius of the circle is 16, so we can substitute this value into the formula and simplify:
C = 2πr
C = 2π(16)
C = 32π
This means that if we were to measure the distance around the perimeter of the circle, we would get a value of 32π units, where π is the irrational number approximately equal to 3.14159.
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Jackson owns a heating and cooling company. He is going to install a new furnace into a customer's house, but he must determine the volume of airflow
needed in order to select the best size of furnace. Find the volume of the house sketched below, where H1-10 ft., H2=9 feet, L=30 feet, and W=20 feet.
Volume of a rectangular prism is V=WLH (width x length x height) Volume of a triangular Prism is:
V =
a.ch
A
A target has a bull's-eye with a d X
O mathwarehouse.com
h (in this case a-9, c= 20, h= 30)
15
[tex]8700[/tex] cubic feet of airflow are required for the entire home. Jackson may utilize this information to determine the best furnace size for the customer's requirements.
Volume explain: What is it?Volume is the quantity of space an object occupies, whereas capacity is a measurement of the substance—such as a solid, liquid, or gas—that an object can hold. While capacity may be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume was determined in cubic units.
What are volume and what is its unit?Volume, which is measured in cubic units, is the three dimensional space inhabited by material or surrounded by a surface. The cubic centimeter (m3), a derived unit, is the SI unit for volume.
Volume of the first section with height [tex]H1=10[/tex] ft:
[tex]V1 = WLH1 = (20 ft)(30 ft)(10 ft) = 6000[/tex] cubic feet
Volume of the second section with height [tex]H2=9[/tex] ft:
[tex]V2 = (1/2)WLH2 = (1/2)(20 ft)(30 ft)(9 ft) = 2700[/tex]cubic feet
Total volume of house,
[tex]V total = V1 + V2 = 6000[/tex] cubic feet + [tex]2700[/tex] cubic feet [tex]= 8700[/tex] cubic feet
Therefore, the volume of airflow needed for the house is [tex]8700[/tex] cubic feet.
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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.x2+y2=100a) Find dy/dt when x=6, y=8 given that dx/dt=4.b) Find dx/dt when x=8, y=6 given that dy/dt=-2.
a) When x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
Using implicit differentiation, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dy/dt, we get:
dy/dt = -(x/y)(dx/dt)
Substituting x = 6, y = 8, and dx/dt = 4, we get:
dy/dt = -(6/8)(4) = -3
Therefore, when x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
b) Using implicit differentiation again, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dx/dt, we get:
dx/dt = -(y/x)(dy/dt)
Substituting x = 8, y = 6, and dy/dt = -2, we get:
dx/dt = -(6/8)(-2) = 1.5
Therefore, when x = 8 and y = 6, and dy/dt = -2, the value of dx/dt is 1.5.
To find the values of dy/dt and dx/dt, we used implicit differentiation, which is a technique used to find the derivative of an equation that is not expressed in the form y = f(x).
In this case, we had the equation x^2 + y^2 = 100, and we differentiated both sides of the equation with respect to t. Then, we solved for the required derivative using the given values of x, y, and the other derivative.
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vertical bar chart that shows frequency on the y-axis [ choose ] population is divided into groups, some groups are selected and all observations from each selected group are included in the sample [ choose ] collection of all data that is of interest [ choose ] a subset or part of a population [ choose ] a sample where the population is divided into groups and several are randomly sampled form each group [ choose ] consists of attributes, labels, or nonnumerical entries [ choose ]
A vertical bar chart that shows frequency on the y-axis is called a histogram. It is a graph showing the distribution of continuous data.
Histograms are used to give an estimate of the probability distribution of a continuous variable sample. Additionally, a subset or part of a population is called a sample. A population is divided into groups, and some groups are selected, and all observations from each selected group are included in the sample. This is called stratified random sampling.
A collection of all data that is of interest is known as the universe.
A collection of attributes, labels, or nonnumerical entries is known as categorical data. This type of data is descriptive in nature, as it allows us to identify what features the data has or belongs to. For instance, age group, gender, and occupation are examples of categorical data. A sample where the population is divided into groups and several are randomly sampled from each group is called a cluster sample. Cluster sampling is an excellent method for conducting a survey when the population is widespread and heterogeneous.
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Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs:
173 191 182 190 172 147 146 139 175 136 179 153 107 195 135 140 138 Fill in the blanks as the data for the five-number summary:
Min = [min] Q1 = [Q1] M = [Median] Q3 = [Q3] Max = [Max]
The five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.
How to find the minimum, maximum?In statistics, the five-number summary is a set of descriptive statistics that provide a summary of the distribution of a dataset. The five-number summary consists of the minimum value, the first quartile (Q1), the median (M), the third quartile (Q3), and the maximum value.
To find the five-number summary for the given data on the number of calories in a hot dog for each of 17 brands of meat hot dogs, we need to order the data from smallest to largest.
107 135 136 138 139 146 147 153 172 173 175 179 182 190 191 195
The minimum value is the smallest value in the dataset, which is 107.
The first quartile (Q1) is the value that is greater than or equal to 25% of the data and less than or equal to 75% of the data. To find Q1, we take the median of the lower half of the data:
Q1 = median(107, 135, 136, 138, 139, 146, 147, 153) = 138
The median (M) is the value that is in the middle of the dataset when the data is ordered from smallest to largest. For the given data, there are 17 values, so the median is the 9th value:
M = median(107, 135, 136, 138, 139, 146, 147, 153, 172, 173, 175, 179, 182, 190, 191, 195) = 175
The third quartile (Q3) is the value that is greater than or equal to 75% of the data and less than or equal to 25% of the data. To find Q3, we take the median of the upper half of the data:
Q3 = median(172, 173, 175, 179, 182, 190, 191, 195) = 190
The maximum value is the largest value in the dataset, which is 195.
Therefore, the five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.
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Line A has a gradient of -5. Line B is perpendicular to line A. a) What are the coordinates of the y-intercept of line B? b) What is the equation of line B? S Give your answer in the form y where m and c are integers or fractions written in their simplest form. mx + c,
The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.
What is equation?An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.
Here,
Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.
a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:
y = (1/5)x + c
0 = (1/5)(0) + c
c = 0
Therefore, the y-intercept of line B is (0,0).
b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.
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Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Question 4(Multiple Choice Worth 2 points)
Answer: 24
Step-by-step explanation:
I don’t know what I’m doing
Answer:
29.12 square cm
Step-by-step explanation:
Area of equilateral triangle:Side = a = 8.2 cm
[tex]\boxed{\bf Area \ of \ equilateral \ triangle = \dfrac{\sqrt{3}}{4}a^2}[/tex]
[tex]\sf = \dfrac{\sqrt{3}}{4}*8.2*8.2\\\\= \sqrt{3}*4.1 * 4.1\\\\= 1.732 * 4.1 *4.1\\\\= 29.12 \ cm^2[/tex]
Ted is five times as old as Rosie was when Ted was Rosie's age. When Rosie
reaches Ted's current age, the sum of their ages will be 72. Find Ted's current age.
Answer:
45 yo
Step-by-step explanation:
Let's start by defining some variables to represent the ages of Ted and Rosie:
- Let's call Ted's current age "T"
- Let's call Rosie's current age "R"
From the problem statement, we know that:
- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:
T = 5(R - (T - R))
Simplifying this equation, we get:
T = 5(R - T + R)
T = 10R - 5T
- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:
R + T = 72 - T
We now have two equations with two variables. We can use substitution to solve for T.
Substitute the second equation into the first equation to eliminate R:
T = 10R - 5T
T = 10(72 - T) - 5T
T = 720 - 15T
16T = 720
T = 45
Therefore, Ted's current age is 45.
[tex]f(x) = \frac{ - 3}{x - 2} + 1[/tex]
Sketch the graph of f clearly showing the asymptotes and the intercepts with the axis
Answer: Vertical asymptote = 2
Horizontal asymptote = 1
y intercept = ( 0, 5/2 )
x intercept = ( 5,0 )
Other points of graph = ( 3,-2 )
= ( 4,-1/2 )
= ( -1, 2 )
= (-2,7/4 )
= ( -3 , 8/5 )
Step-by-step explanation:
a blackboard of sides 5 M 30 cm and 3m 20 CM has to be painted find the cost of the rate of rs 15 per m².
Answer: The cost of painting is Rs.254.4
Step-by-step explanation:
let l and b be the sides
here l= 5m 30cm=5.30mb=3m 20 cm=3.20m
Area of blackboard = l×b= 5.30×3.20
=16.96m²
cost of painting per m² = 15 rscost of painting per 8.5m² = 16.96 × 15 =254.4 rs
We are given that, the measures of sides of blackboard are 5 m 30 cm and 3m 20 cm.
__________________________________________
Length of the Blackboard[tex] \bf \implies5 m + 30 cm \\ [/tex]
[tex] \sf \implies 5 m + \dfrac{30}{100}m \\ [/tex]
[tex] \sf \implies 5 m + \dfrac{3\cancel{0}}{10\cancel{0}}m \\ [/tex]
[tex] \sf \implies 5 m + 0.3 m \\ [/tex]
[tex]\purple{ \bf \implies 5.3~ m } \\ [/tex]
Breadth of the Blackboard[tex] \bf \implies3 m + 20 cm \\ [/tex]
[tex] \sf \implies 3 m + \dfrac{20}{100}m \\ [/tex]
[tex] \sf \implies 3 m + \dfrac{2\cancel{0}}{10\cancel{0}}m \\ [/tex]
[tex] \sf \implies 3 m + 0.2 m \\ [/tex]
[tex] \purple{\bf \implies 3. 2 ~m} \\ [/tex]
_______________________________________________
[tex] \pink{\frak{\implies Area _{(Blackboard) }= Length \times Breadth ~m^2}} \\ [/tex]
[tex] \sf \implies Area _{(Blackboard) } = 5.3 \times 3.2 ~m^2 \\ [/tex]
[tex] \sf \implies Area _{(Blackboard) } = 16.96 m^2 \\ [/tex]
Henceforth, the cost of the rate of rs 15 per m² will be -[tex] \sf \implies 15 \times 16.96 \\ [/tex]
[tex] \pink{\sf \implies Rs ~254.4 } \\ [/tex]
The number of employees for a certain company has been decreasing each year by 5%. If the company cumently has 860 employees and this rate continues, find the number of employees in 10 years
The number of employees in 10 years will be approximately
(Round to the nearest whole number as needed)
Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.
What is exponential decay equation?The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.
Exponential decay equation is one of the two exponential functions. The other is the exponential growth equation.
The annual decrease in the number of employees = 5%
The current number of employees in the company = 860
The expected time = 10 years.
The exponential decay equation is as follows, y = 860 x 0.95^10.
y = 860 x 0.95^10 = 515
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Let f(x) = (x - 1)2,g(x) = e-2 , and h(x) = 1 In(1 2x) _ (a) Find the linearizations of f, g, and h at a = 0
Lf(x)=1-2x
Lg(x)=1-2x
Lh(x)=1-2x
Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
The linear approximation appears to be the best for the function (f, g, or h *h is not the answer) since it is closer to (f, g, or h) for a larger domain than it is to (f and g, g and h, f and h). The approximation looks worst for (f, g, or, h) since (f, g, or, h) moves away from L faster than (f and g, g and h, f and h) do.
We can see that the linear approximation appears to be the best for function g since it is closer to g for a larger domain than it is to f and h. The approximation looks worst for function f since f moves away from Lf faster than g and h do. Hence, the linear approximation is the worst for function f.
Given that f(x) = (x - 1)^2, g(x) = e^(-2), and h(x) = ln(1+2x) - 2x.
(a) Find the linearizations of f, g, and h at a = 0.
The linearization of f at a = 0 is given by
Lf(x) = f(0) + f'(0)(x - 0)
= (0 - 1)^2 + 2(0 - 1)(x - 0)
= -x + 1
The linearization of g at a = 0 is given by
Lg(x) = g(0) + g'(0)(x - 0)
= e^(-2) + 0(x - 0)
= e^(-2)
The linearization of h at a = 0 is given by
Lh(x) = h(0) + h'(0)(x - 0)
= (ln(1 + 2(0)) - 2(0)) + [(1/(1 + 2(0)))2 - 2](x - 0)
= -2x
Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
The graphs of f(x) = (x - 1)^2, g(x) = e^(-2), h(x) = ln(1+2x) - 2x, and their respective linear approximations Lf(x) = -x + 1, Lg(x) = e^(-2), and Lh(x) = -2x.
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How much would it cost to buy a sheet of a metal 4m by 75cm which cost E90 to a metal of 5m by 2m
It would cost €27 to buy a sheet of area 4 meters by 75 centimeters.
We solve this problem easily by employing the unitary method. To answer this question, we need to first calculate the area of the metal sheet being sold and the area of the metal sheet being purchased.
The area of the metal sheet being sold is:
5 meters × 2 meters = 10 square meters
The area of the metal sheet being purchased is:
4 meters × 0.75 meters = 3 square meters
Now we can calculate the price per square meter of the metal sheet being sold:
€90 ÷ 10 square meters = €9 per square meter
Finally, we can calculate the cost of the metal sheet being purchased:
3 square meters × €9 per square meter = €27. Therefore, the cost to buy a sheet of area 4 meters by 75 centimeters which costs €90 to a metal of area 5 meters by 2 meters would be €27.
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Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck
Answer:
Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck
Step-by-step explanation:
Let's start by subtracting the base fee from the total cost:
$143.43 - $16.95 = $126.48
Now, we can divide the remaining cost by the cost per mile:
$126.48 ÷ $0.93/mile ≈ 136 miles
Therefore, Stacy drove the truck for approximately 136 miles.
The triangles are similar find the value of X
Answer:
x = 36
Step-by-step explanation:
[tex] \frac{12}{14} = \frac{x}{42} [/tex]
[tex]x = 36[/tex]
[tex]42 \div 14 = 3[/tex]
[tex]3 \times 12 = 36[/tex]
The ____________ assumption requires that all variation around the regression line should be equal at all possible values (levels) of the ___________variable.
A. control variance, dependent
B. constant variance, independent
C. constant variance, dependent
D. control variance, independent
The B) constant variance assumption requires that all variation around the regression line should be equal at all possible values (levels) of the independent variable.
The constant variance assumption, also known as homoscedasticity, requires that the variance of the residuals (i.e., the differences between observed and predicted values) should be approximately the same across all levels of the independent variable.
This assumption is necessary for valid statistical inference in linear regression analysis because violations of constant variance can result in biased estimates of the regression coefficients and incorrect hypothesis tests.
The independent variable is the variable that is used to predict the dependent variable. The constant variance assumption applies to the residuals at all possible values of the independent variable. Therefore, the correct answer is B. constant variance, independent.
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Suppose that a fair, 6 sided die is rolled. Let X indicate the event that an odd number is rolled in other words, X = 1 if an odd number is rolled and X = 0 otherwise). Let Y indicate the event that 3, 4, or 5 is rolled (in other words, Y = 1 if 3, 4 or 5 is rolled and Y = 0 otherwise). Find P(X = 0, y = 1). a. 2/3 b. 176 C.1/3 d. 5/6 e. 1/2
Option (c) 1/3 is the correct answer.Let us first understand the given problem,It is given that the fair 6-sided die is rolled and let X indicates the event that an odd number is rolled and Y indicates the event that 3,4, or 5 is rolled.
P(X=0,Y=1)Solution:When an odd number is not rolled, then an even number is rolled. So, the possible even numbers that can be rolled on a die are 2,4 and 6. Therefore,X = 0, when an even number is rolledY = 1, when 3, 4 or 5 is rolledLet's find P(X=0,Y=1).P(X = 0, Y = 1) = P(rolling 4) = 1/6The sample space for a fair die will be {1,2,3,4,5,6}.
The odd numbers are {1,3,5}. Therefore,P(X = 1) = probability of getting an odd number= 3/6 = 1/2 (3 possible odd numbers out of 6)P(X = 0) = probability of getting an even number= 3/6 = 1/2 (3 possible even numbers out of 6)P(Y = 1) = probability of getting 3, 4, or 5= 3/6 = 1/2 (3 possible numbers out of 6)P(Y = 0) = probability of getting 1, 2, or 6= 3/6 = 1/2 (3 possible numbers out of 6)P(X = 0, Y = 1) = P(rolling 4) = 1/6. Therefore, P(X=0, Y=1) = 1/6Therefore, option (c) is correct.
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Maria state that (-4,2) (2,4),(2,-2),(-4,-1) are the coordinate pairs of the vertices of her figure
If Maria state that (-4,2) (2,4),(2,-2),(-4,-1) are the coordinate pairs of the vertices of her figure, then the area of her quadrilateral figure is equals to the 9 sq. units.
A quadrilateral is a four-sided and 2D geometrical figure whose sum of all the four internal angles is 360°. Also, it has 4 edges and four vertices (or corners). Let's consider the vertices of a quadrilateral ABCD be A( x₁,y₁), B(x₂,y₂), C(x₃,y₃), D(x₄,y₄). The area of quadrilateral ABCD is written as A = (1/2) |(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) – (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)|
Now, Maria defines a quadrilateral with the following vertices (-4,2),(2,4),(2,-2),(-4,-1). After comparing these vertices with (x₁,y₁),(x₂,y₂), (x₃,y₃), (x₄,y₄), we see, x₁ = -4 ,y₁ = 2, x₂ = 2, y₂ = -2, x₃ = 2, y₃ = -2, x₄ = -4, y₄ = -1. Substitute all known values into above formula, Area of her quadrilateral figure, A = (1/2)|((-4)(-2) + 2(-2) + 2(-1) + (-4)2) – (2×2 + 2×(-2) + (-4)(-2) + (-4)(-1))|
= (1/2)|( 8 - 4 - 2 - 8) - (4 - 4 + 8 + 4)|
= (1/2)|-6 - 12| = 9 sq. units
Hence, required area of quadrilateral is 9 sq. units.
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Complete question:
Maria states that (-4,2) (2,4),(2,-2),(-4,-1) are the coordinate pairs of the vertices of her figure. Calculate the area of her figure.
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The correct answer is p=62
Daniel is paid an hourly rate of $9. 00 plus six percent commission on direct phone sales. Last week he worked 48 hours and received $72. 00 in commissions. What was his pay for the week?
Daniel's pay for the week was $504.00, which includes his hourly pay and his commission on direct phone sales.
To calculate Daniel's pay for the week, we need to find his total earnings, which include his hourly wage and his commission on direct phone sales.
First, let's calculate his commission on direct phone sales. We know that he received $72.00 in commissions, and we also know that his commission is six percent of his sales. So, we can use the formula:
Commission = Sales x Commission Rate
To find his sales, we can rearrange the formula to:
Sales = Commission / Commission Rate
Plugging in the given values, we get:
Sales = $72.00 / 0.06 = $1200.00
So, Daniel's direct phone sales for the week were $1200.00.
Now, let's calculate his hourly pay. He worked for 48 hours at a rate of $9.00 per hour, so his hourly earnings were:
Hourly Pay = Hours Worked x Hourly Rate
Hourly Pay = 48 x $9.00 = $432.00
Finally, we can add his commission and his hourly pay to find his total earnings for the week:
Total Pay = Hourly Pay + Commission
Total Pay = $432.00 + $72.00
Total Pay = $504.00
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two fifths of 60 is what number
Answer:
I hope this helps please rate my answer
Step-by-step explanation:
2/5×60
2×12=24
write the hypotheses to test if the success rate for art at this clinic is significantly higher than the success rate reported by the cdc.
In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.
what is null hypothesis ?A claim or assumption that there is no statistically significant difference between two populations or sets of data is known as the null hypothesis. It serves as the beginning point for statistical hypothesis testing and is typically indicated as H0. According to the null hypothesis, any observed difference between the populations or data sets is the result of sampling error or random chance rather than a genuine difference.
given
The success rate for art at this clinic is not statistically different from the CDC's claimed success rate.
In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.
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You construct three 88% confidence intervals as follows: A) A t-interval with 6 degrees of freedom. B) A t-interval with 2 degrees of freedom. C) A z-interval Assuming the mean and standard deviation are the same for all three intervals, write the three intervals (A, B, and C) in order, from narrowest to widest.
The order from narrowest to widest is: C) z-interval. A) t-interval with 6 degrees of freedom. B) t-interval with 2 degrees of freedom.
What is confidence interval?In statistics, the likelihood that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations. So, it may be concluded that there is a 95% likelihood that the real value falls within that range if a point estimate of 10.00 with a 95% confidence interval of 9.50 - 10.50 is derived using a statistical model.
A confidence interval's breadth is influenced by the sample size and degree of confidence. Higher confidence levels often result in broader intervals, whereas bigger sample numbers typically result in narrower intervals.
In this instance, the three intervals have different degrees of freedom but the same 88% confidence level.
Hence, The order from narrowest to widest is: C) z-interval. A) t-interval with 6 degrees of freedom. B) t-interval with 2 degrees of freedom.
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