The other leg has its length to be 11.49 units
How to determine the length of the other leg distance?To calculate the length of the other leg distance, we make use of the Pythagoras theorem
Mathematically, this theorem is represented by:
w² = y² + z²
Such that x = hypotenuse, y = leg and z = other leg
From the question, we have the following parameters
w = 14, y = 8 and z = the other leg
Substituting these values in w² = y² + z²
14² = 8² + y²
Evaluate the exponents
196 = 64 + y²
Evaluate the like terms
y² = 132
Take the square roots of both sides
y = 11.49
Hence, the length of the other leg is 11.49 units
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Answer: 11 units
Step-by-step explanation: i took the test and got it right
Write an equation of a line that passes through (-1,2) and is parallel to a line with x-intercept (3,0) and y-intercept (0,1).
The Equation of line is y= -1/3x + 5/3
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
x-intercept = (3,0) and y-intercept = (0,1).
slope, m= 0-1/ 3-0= -1/3
so, The slope-intercept form of the equation of a line is
y= mx + b
y= -1/3x +b
Now, the passes through (-1, 2) we get
2= -1/3(-1) + b
2- 1/3= b
b= 5/3
So, the Equation of line is y= -1/3x + 5/3
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Ester sarai and kurry chose a number esters number is 1/10 of saris kurrys number is 10 times as much as sarais sarais number is 0.09. what number did each person choose?
Ester, Sarai, and Kurry each selected a number: 0.009, 0.09, and 0.9, respectively.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes. For instance, 3+3+3+3+3 can be expressed as 3 5.
the ester's number is equal to one-tenth of the Sarai number.
= 1 / 10 × 0.09 = 0.009
to determine Kurry's number, multiply Sarai's number by 10
= 10 × 0.09 = 0.9
Therefore, it can be inferred that Kurry chose 0.9, Ester chose 0.009, and Sarai chose 0.09.
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In a company, 85% of the workers are women. If 675 people work for the company who aren't women, how many workers are there in all?
Answer:
so there are 3825 worker in total
Step-by-step explanation:
675=15%
women=85%
how much workers are 5%=675/3 =225
225=5%
how many workers is 85%= 85/5=17
85%=225x17=3825
Latisha wants to buy pumpkins and autumn squash for a fall display. She has a budget of $117 but wants to buy more than 10 vegetables. The pumpkins are $5. 59 each. The squash are $3. 50 each. List THREE possible combinations of pumpkins and squash that latisha can purchase to represent the situation
(x,y) = (8,20), (6,24), and (10,17).are three alternative combinations of pumpkins and squash that Latisha may buy to depict the circumstance.
Latisha's total wealth is $17.
More than 10 veggies are the number of vegetables that Latisha wants to purchase.
A pumpkin costs $5.50.
An autumn squash costs $3.50.
Let n pumpkins purchased equal x.
Purchased number of autumn squash = y
There are three alternative squash and pumpkin combination that Latisha might buy to symbolize the circumstance.
With x acting as the independent variable, we may identify many y's.
x ( Pumpkin) y(Autumn squash) (integral value)
8 20
6 24
10 17
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Zachary is applying biomechanics to develop a specialized bat for a professional player. What does he compar
the hitter to?
Oa machine
O a computerized model
O another professional player
O a 3-D diagram
Answer:
Another Professional Player
suppose 44% of politicians are lawyers. if a random sample of size 853 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 40%? round your answer to four decimal places.
The probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
Given :
Population Proportion ( p ) = ( 44 % ) = 0.44
Sample proportion ( p hat ) = ( 40 % ) = 0.4
Size of sample ( n ) = 853
To find : P ( p hat < 0.4 )
Formula : ( p hat - p ) / [tex]\sqrt{ p * ( 1 - p ) / n }[/tex]
Substituting values in the above formula ,
z = ( 0.4 - 0.44 ) / [tex]\sqrt{ 0.44 * ( 1 - 0.44 ) / 853}[/tex]
z = - 2.3535
z - score = -2.3535
Finding the p - value :
p - value = 0.009299
Therefore , the probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
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Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer: 0.86 pounds of fruit
Step-by-step explanation:
8.3-7.44=0.86
A triangle has an angle that measure 36.6° and a second angle that measures 59.3°. What is the
measure of the third angle?
2 pts
Answer: 82 is the answer
Step-by-step explanation: I just did this question and worked it out and it said it was right
y = 1,000x is that a constant proportionality
/what is y-5x=3 solve for Y
Answer:
y=3+5x
Step-by-step explanation:
Add 5x to both sides.
Which statement is true?
This table does not show a probability distribution.
This table shows a probability distribution.
After using the probability distribution table, the given table does not show a probability distribution. The statement 1 is correct.
In the given question, we have to check which statement is correct regarding to the given option.
The given statements are:
(1) This table does not show a probability distribution.
(2) This table shows a probability distribution.
Before checking the statement we learn about a probability distribution table.
In a probability distribution table every result of a statistical experiment is connected to the likelihood that the result will actually occur. An experiment's result is recorded as a random variable, which is typically written with a capital letter.
As we can see that there is given the probability of having the blue, green, yellow and red color.
So the given table does not show a probability distribution.
So the statement 1 is correct.
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What is the equation in standard form of the line that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y=1
The required equation of line in standard form that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y = 1 is
y = (3/8)x - 13/4
How to find equation of line if one point and equation of perpendicular line is given?
To find the equation of line which is perpendicular to another line
Find slope of the required line using m₁. m₂ = -1Using the given point find y-intercept by substituting in the equation of line.According to the given question:
Let the required equation of line be y = mx + b
where m is the slope of line and b is the y-intercept
Now, 8x + 3y = 1 is perpendicular to the line. Hence, the slopes of both line will satisfy m₁. m₂ = -1
Standard form of the given line is
y = (-8/3)x + 1/3
∴ m₁ = -8/3
Finding m₂, (-8/3). m₂ = -1
∴ m₂ = 3/8 ------ (1)
Using the given point (6, -1) to find y-intercept in the equation
y = (3/8)x + b
-1 = (3/8)(6) + b
∴ b = -13/4
Therefore the required equation of line in standard form is
y = (3/8)x - 13/4
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two trains leave a station at the same time and travel in opposite directions. one train travels 20 kph faster than the other train. after 3 hours, they are 810 miles apart. what is the speed of each train?
The speed of each train is 125kph and 145kph.
Here it is given that the distance between the two trains is 810 miles after traveling for 3 hours.
The difference in their speed is 20 kph.
Let x be the speed of one train. So by this, we get the speed of the second train that is x + 20.
Formula to calculate speed is:
Speed = Distance / Time
Distance = Speed × Time
Distance covered by first train = x × 3
Distance covered by second train = (x + 20) × 3
Total distance = 810
So we get;
3x + (x + 20)3 = 810
3x + 3x + 60 = 810
6x = 750
x = 125
x + 20 = 125 + 20 = 145
Therefore we get the speed of both trains which is 125kpp and 145 kph.
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Please help now asap !!! Due tomorrow
Answer:
Step-by-step explanation:
it help by showinbng thta
Walt Disney Co paid a $1.42 annual dividend on a day it closed at a price of $96 per share.
What was the annual dividend for 500 shares?
The annual dividend for 500 shares was $710.
How is the annual dividend computed?The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.
Dividends are always declared per share with a stated dollar amount or percentage.
Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.
Dividends are a kind of financial reward to stockholders for their investment in the entity.
The dividend per share = $1.42
Market price per share = $96
The number of shares held = 500
The dividend received for the year = $710 ($1.42 x 500)
Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.
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1. which of these variables are discrete and which are continuous random variables? (a) the number of new accounts established by a salesperson in a year. (b) the time between customer arrivals at a bank atm. (c) the number of customers at big nick's barber shop. (d) the amount of fuel in your car's gas tank. (e) the number of minorities on a jury. (f) the outside temperature today.
The discrete and continuous random variables are-
a) Discrete; (b) Continuous; (c) Discrete; (d) Continuous; (e) Discrete; (f) Continuous
Define the term discrete and continuous random variables?Discrete variables are those whose values may be measured through counting. Contrarily, random variables which it reflect something are designated continuous variables.(a) So because number of new accounts is counted, (a) discrete (like, non-negative integers).
(b) Continuous, given that the interval between customer arrivals may have decimal values (like 2.9 minutes or 27.75 seconds).
(c) Because the quantity of clients is counted, (c) discrete (like, non-negative integers).
(d) Continuous, as the fuel consumption can have decimal values (like 15.5 gallons).
(e) Since this number of minorities is counted, (e) discrete (like, non-negative integers).
(f) Continuous since the outdoor temperature can be expressed in decimal degrees (e.g., 7.78 C).
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The proportional relationship between the cost and weight is given as y = 0.89x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The absolute expense for clothing administration, in dollars, relies upon the heaviness of the clothing, in pounds. This relationship is corresponding, as it costs $22.25 for 25 pounds of clothing and $36.49 for 41 pounds of clothing.
The equations are given below.
22.25 = 25m + c ...1
36.49 = 41m + c ...2
From equations 1 and 2, then we have
41m - 25m = 36.49 - 22.25
16m = 14.24
m = 0.89
Then the value of c will be given as,
22.25 = 25 (0.89) + c
c = 0
The proportional relationship between the cost and weight is given as y = 0.89x.
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what is the definition of pi
and multiply it to a decimal number
(any equation)[tex]\pi[/tex]
Pi written as 3.l4 and π in mathematics is the ratio for the diameter of a circle to the circumference of that circle. The value is unending
What is Pi?Pi, which is represented by the Greek letter p, or, is a shorthand for the ratio of a circle's diameter to its circumference. No matter how big the circle is, this ratio will always be equal to pi. The value of pi is about 3.14 in decimal notation.
We are to multiply Pi to any equation
let the equation be (20.5 + 3x)[tex]\pi[/tex]
pi is represented in numbers by 3.14
Hence we would have the equation to be of the form
(20.5 + 3x)3.14
multiply through the bracket
64.37 + 9.42x
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Trapezoid G is a scaled copy of trapezoid F.
Answer:
yes it is???
Step-by-step explanation:
Use the rules of measurement to divide
Answer:
[tex] \frac{ {m}^3{} }{25} [/tex]
Step-by-step explanation:
that is the answer
The sum of two numbers is 12. The difference of the same two numbers is -4. Wht is the smaller number?
Answer:
The smaller number is 4.
Step-by-step explanation:
X and Y are the two numbers
x+y=12
x-y=-4
Subtract these two equations
(x+y=12)
-(x-y=-4)
—————-
2y=16
y=8
Plug it in to any equation:
x+y=12
x+8=12
x=4
You're putting 81 feet of molding
along the walls around a rectangular
room that's 12 feet wide; what is the
area of that room (if you subtracted
3 feet for the width of the door)?
Answer:
360 sq feet
Step-by-step explanation:
The width of the room is given in the question, 12 feet.
We don't know the length. Let's call the length x.
x = length
We were also given the perimeter, 81, that's the distance around the sides...
all the sides added up.
Use x for the long wall.
Use x-3 for the wall with the door in it.
x + 12 + x-3 + 12 = 81
combine like terms
2x + 21 = 81
subtract 21
2x = 60
divide by 2
x = 30
The room is 30 feet long by 12 feet wide.
Area =
length × width
= 30 × 12
= 360
The area of the room is 360sq feet.
Find m∠1 and m∠2. Tell which theorem can be used.
According to the vertical angles theorem, m∠1 = 117°.
Based on the corresponding angles theorem, m∠2 = 117°.
What is the Vertical Angles Theorem?The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.
What is the Corresponding Angles Theorem?When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.
Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.
Therefore:
m∠1 = 117° [vertical angles theorem]
Angles 1 and 2 are corresponding angles. Therefore:
m∠2 = m∠1
Substitute
m∠2 = 117° [corresponding angles theorem]
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The polynomial f(x) = 2x ^ 3 + a * x ^ 2 + bx + 6 is exactly divisible by 2x - 3 and has the remainder -28 when divided by (x + 3) a) find the values of a and b. b) solve the equation f(x) = 0
The polynomial f(x) = 2x³ + ax² + bx + 6 is exactly divisible by 2x - 3. The values of a and b are a = 131/27 and b = -71/9
To solve the problem, use the polynomial remainder theorem. If a polynomial f(x) is divided by a linear function with zero x = a, then the remainder r = f(a).
The given polynomial is:
f(x) = 2x³ + ax² + bx + 6
- The polynomial is exactly divisible by (2x-3) means:
f(3/2) = 0
2. (3/2)³ + a(3/2)² + b(3/2) + 6 = 0
27 + 9a + 6b + 24 = 0
9a + 6b = - 51 (equation 1)
- f(x) divided by (x+3) has remainder -28
f(-3) = -28
2. (-3)³ + a(-3)² + b(-3) + 6 = -28
9a - 3b = 20 (equation 2)
Substract equation 2 from equation 1
9a + 6b = -51
9a - 3b = 20 _
9b = -71
b = -71/9
9a - 3(-71/9) = 20
9a = 131/3
a = 131/27
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The functions f(x)=−34x+2 and g(x)=(14)x+1 are shown in the graph. What are the solutions to −34x+2=(14)x+1? Select each correct answer. Responses −1 negative 1 0 0 1 1 2 2 3
A solution to −34x+2=(14)x+1 is x = 1/48
In this question, we have been given functions f(x) = -34x + 2 and g(x) =(14)x + 1
We need to find the solutions to −34x + 2 = (14)x + 1
i.e., we need to find the solution to f(x) = g(x)
Consider, f(x) = g(x)
-34x + 2 = (14)x + 1
-34x + 2 - 14x = 14x + 1 - 14x
-48x + 2 = 1
-48x = -1
x = 1/48
Therefore, a solution to −34x+2=(14)x+1 is x = 1/48
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d) The rent of a room for 4 months is Rs 20,000. (i) What is the rent for 7 months? (ii) How long would a tenant hire the room for Rs 55,000 at the same rate of rent?
The rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
The rent of a room for 4 months is Rs 20,000.
The rent of a room for 1 month is Rs 20,000./4
The rent of a room for 1 month is Rs 5000
The rent of a room for 7 months is Rs 5000 x 7
The rent of a room for 7 months is Rs 35000
Now we need to calculate the number of month a tenant hire the room for Rs 55,000 at the same rate of rent
The rent is 5000 for 1 month
The rent will be 55000 for 1/5000 x 55000 = 11 months
Therefore, the rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
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PLEASE HELP!! WILL GIVE BRAINLIEST
The mass of a test sample is 10g, and it has the volume of 2.5cm^3 . What is its density?
A. 10g/cm^3
B. 2.5cm^3/g
C. 4g/cm^3
D. 4cm^3/g
E. 0.25g/cm^3
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
Define density.The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.
Given,
Volume = 2.5 cm³
Mass = 10 g
For density:
Mass ÷ volume
10 ÷ 2.5
4
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
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A runner completed a 26.2-mile
marathon in 210 minutes.
a. Estimate the unit rate, in miles per minute.
b. Estimate the unit rate, in minutes per mile.
c. Another runner says, “I averaged 10-minute miles in the
marathon.” Is this runner talking about the unit rate
described in part (a) or in part (b)? Explain your reasoning.
Step-by-step explanation:
The answer is: A=210÷26.2=8.2
B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7
Answer:
A) 26.2/210= .125 miles per minute
B) 210/26.2= 8.02 minutes per mile
C) the other runner talks about the same rate as b), not a).
Step-by-step explanation:
A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)
C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.
If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.
During the problem disaggregation process, the logic trees should have branches that are?.
During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.
Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.
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Corinne and Deanna decide to race from one corner of an open field to the other. The field is rectangular in shape, 60 meters long and 80 meters wide. Since Corinne is older and faster, she's going to run along the outside of the field, and Deanna will take the diagonal route. If Deanna can run at a rate of 5 meters per second, how fast will Corinne have to run to get there at the same time as Deanna?
Answer:
Corinna will have to run at 7 meters per second to get there at the same time as Deanna.
Step-by-step explanation:
So to find the distance of Deanna's route, you can use the Pythagorean theorem.
a^2 + b^2 = c^2
60^2 + 80^2 = 10000
c^2 = 10000
Take the square root of both sides.
c = 100
So Deanna runs 100 meters at 5 meters per second.
100/5 = 20
She runs for 20 seconds.
To find Corinne's distance, we add 60 and 80, which is 140.
To find how fast she need to run to get there in 20 seconds, you divide 140 by 20, which gets 7 (meters per second). You can also think of it like this: to run 140 meters in 20 seconds, she has to run at 140 meters per 20 seconds, which you can simplify (like a fraction) to 7/1, or just 7