The town and PSA are (a) 10 units apart
How to determine how far they are apartFrom the question, we have the following parameters that can be used in our computation:
Points = (2, 3) and (-4, -5)
The distance between the two towns can then be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
substitute the known values in the above equation, so, we have the following representation
distance = √[(2 + 4)² + (3 + 5)²]
Evaluate
distance = 10
Hence, the distance apart is 10 units
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Mr. Molesky and Mr. Liberty are avid video game golfers. Both like to compare times to complete a
110 minutes and standard deviation of 10 minutes. Mr. Liberty's times are Normally distributed with
particular course on their favorite game. Mr. Molesky's times are Normally distributed with a mean of
mean 100 minutes and standard deviation 8 minutes.
a) Find the mean and standard deviation of the difference of their times (Molesky - Liberty). Assume
their times are independent.
b) Find the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day.
Answer: a) To find the mean and standard deviation of the difference of their times, we need to use the properties of normal distributions. When two independent normal random variables are subtracted, the mean and standard deviation of the difference can be found using the following formulas:
Mean of the difference = Mean of x - Mean of y
Standard deviation of the difference = √(Standard deviation of x^2 + Standard deviation of y^2)
Plugging in the given values:
Mean of the difference = Mean of Molesky - Mean of Liberty = 100 - 110 = -10
Standard deviation of the difference = √(8^2 + 10^2) = √(64 + 100) = √(164) = 12.8
So the mean of the difference of their times is -10 minutes and the standard deviation is 12.8 minutes.
b) To find the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day, we need to find the probability that the difference of their times is less than 0. Since the difference of their times is normally distributed with a mean of -10 and a standard deviation of 12.8, we can use the standard normal distribution table to find this probability.
To calculate the probability, we will standardize the distribution of the difference by subtracting the mean and dividing by the standard deviation.
z = (x - mean) / standard deviation
z = (-10) / 12.8 = -0.78125
Using a standard normal table we can find that P(z<-0.78125) = 0.22 or 22%
So the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day is 22%.
Step-by-step explanation:
true or false: pooled variance is used for an inference about two means for two small independent samples when we assume normal population with equal variance.
It is true that Pooled variance is used for an inference about two means for two small independent samples when we assume normal population with equal variance.
Pooled variance is a statistical method used to estimate the common variance of two small independent samples when the population variances are assumed to be equal.
The pooled variance is calculated by taking the weighted average of the variances of the two samples.
This method is often used in inferential statistics to make inferences about the means of the two populations from which the samples were drawn.
The pooled variance is used to estimate the variance of the difference between the means of the two populations, which is used to calculate the standard error and the t-statistic for testing the difference between the means. Therefore, The statement is true.
so, It is true that Pooled variance is used for an inference about two means for two small independent samples when we assume normal population with equal variance.
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If ABCD is a parallelogram, what is the length of BD?
B
с
5
7.
E
6
А
D
The length of diagonal BD from the parallelogram ABCD is 10.
E is the intersection of the diagonals BD and AC. The point of bisection is therefore designated E.
BE = DE (The diagonals of a parallelogram bisect each other) (The diagonals of a parallelogram bisect each other)
From the provided diagram:
BE = 5
DE = BE = 5
BD length equals BE plus DE
BD length equals (5 + 5) to 10.
ABCD is a parallelogram, what is the length of BD
Consequently, Diagonal BD is 10 in length.
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the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w if it takes 10 hours to paint 400 feet of fence with six workers how long it will take for 10 workers to paint 1000 ft fence
Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
What is proportionality constant?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.
Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.
This is represented as follows:
t = k(l/p)
Where, k is the proportionality constant.
Given that, it takes 10 hours to paint 400 feet of fence with six workers.
Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:
10 = k (400 / 6)
10 = k (66.66)
k = 10 / 66.66
k = 0.15
Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:
t = (0.15) (1000 / 10)
t = (0.15) (100)
t = 15
Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
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Find the equation of the line with y-intercept - 6 and slope - 6 over 7
It can be written as
y = -6/7x - 6/7 * x1 + y1
What is the slop?
The slope, also known as the gradient, is a measure of the steepness of a line. It tells us how much the y-coordinate of a point on the line changes as the x-coordinate changes. The slope is often represented by the letter "m" in the equation of a line. The slope is defined as the ratio of the rise (the change in y-coordinate) to the run (the change in x-coordinate) between two points on a line.
An equation of a line in slope-intercept form is:
y = mx + b
where:
m = slope of the line
x = variable of the line
y = variable of the line
b = y-intercept
Given the y-intercept is -6 and the slope is -6/7, we can substitute these values into the equation above:
y = -6/7x + -6
This equation of the line is in slope-intercept form, and it can be used to find the y-coordinate of any point on the line given the x-coordinate, or to find the x-coordinate of any point on the line given the y-coordinate.
You can also write it in point-slope form.
The point slope form is
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line.
So it can be written as
y = -6/7x - 6/7 * x1 + y1
Where the x1 and y1 are arbitrary value which lies on the line.
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PLEASE HELP 100 POINTS!!
A line has a slope of 0 and a y-intercept of –5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
the answer is 0= -5/3x + c
Answer: non
as a wordf 2 b geven
10. A warehouse has 2,100 tables packaged in boxes. They ship 25 tables daily. After how many days will there be fewer than 1,500 tables in the warehouse? Solve and graph the inequality.
The number of days that it will take for there to be fewer than 1,500 tables in the warehouse is given as follows:
More 24 days.
How to solve the inequality?The initial number of tables is given as follows:
2,100 tables.
They ship 25 tables daily, hence the function for the number of tables after n days is given as follows:
T(n) = 2100 - 25n.
There will be fewer than 1,500 tables after n days, for which;
T(n) < 1500
Hence:
2100 - 25n.< 1500
25n > 600
n > 600/25
n > 24.
Hence the time is more than 24 days.
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Jayden bought 70 feet speaker wire for $18. 20 he needed 30 more feet if the unit price is the same how much will jayden Pay for an extra 30 feet of wire
For the extra 30 feet of wire Jayden have to pay an amount of $7.80 at a rate of $0.26 per feet.
In these type of problems, first we have to find out the unit price. First let's look at what data is available.
The length of wire Jayden bought = 70 feet
Amount Jayden paid for 70 feet = $ 18.20
Unit price or price of 1 feet of speaker wire = Amount paid / length bought.
Unit price = 18.20/ 70 = 0.26.
So he have to pay 26 cents for each foot of wire.
Now let's calculate the amount for 30 feet of wire = Unit price × 30 = 0.26×30 = 7.80.
So Jayden have to pay $7.80 for the extra 30 feet of wire.
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Three of these pairs of quantities are related by direct variation. Which pair is NOT?
A. x=hours traveled at 60 miles per hour, and y= total distance traveled
B. x=length of a rectangular table, in inches, and y=length of the table, in centimeters
C. x=number of $1-off coupons used, and y=amount saved
D. x=time it takes to travel 60 miles, and y=speed traveled
If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.
Which pairwise relationship between the quantities best represents direct variation?If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.
The direct variation equation is represented by the symbols y=kx or k=y/x, where k is the proportionality constant or variation constant.
A) The relationship between the distance traveled and the number of traveled hours is straightforward.
B ) The only distinction between x and y representing the length of a table is in units.As a result, it also differs directly.
The amount of money saved in C increases as more $1-off coupons are used, and vice versa.
If the speed is increased in D, it will take less time to travel 60 miles.As a result, there is no direct variation.
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Rita lent rs6800 for 5 years at 5% p. A. Interest , whereas mita lent rs 8600 for 4 year at 4%. Who earned more interest and by how much
Based on the investment amount, rate of interest and time, Rita earned more interest than Mita by $324.
Calculating simple interest in both the cases to find the earned interest. The formula for simple interest is as follows -
S.I. = PRT/100, where S.I. is simple interest, P is principal, R is rate of interest and T is time.
Interest earned by Rita -
S.I. = 6800 × 5 × 5/100
Performing multiplication and cancelling zero
S.I. = $1700
Interest earned by Mita -
S.I. = 8600 × 4 × 4/100
Performing multiplication and cancelling zero
S.I. = $1376
Difference in interest = Interest earned by Rita - Interest earned by Mita
Difference in interest = 1700 - 1376
Performing subtraction
Difference in interest = $324
The interest earned by Rita is more than the interest earned by Mita by $324.
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What are given?Php 45.50 - cot of 1 kilo of mango Php 35.00 - cot of a pineapple Php 19.50 -change Php100.00-Amount given to the fruit vendor with olution
It is right to receive a change of 19.50 if Juan gave php 100.00 to the fruit vendor
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Mango = 45.50Pineapple = 35.00Amount given = 100Calculating how many Juan spend we have:
Total cost = mango + pineapple
Total cost = 45.50 + 35.00
Total cost = 80.5
Calculating how much Juan should receive in change:
Change = Amount given - Total cost
Change = 100 - 80.5
Change = 19.5
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Correctly written question:
Juan bought a kilo of mango at 45.50 and pineapple at 35.00 is it right to receive a change of 19.50 if he gave php 100.00 to the fruit vendor?
if s represents the number of scarves sold and h represents the number of hats sold, which system of equations represents the constraints in this situation?
If knitting club sold 40 scarves and hats at a winter festival and made $700 from sales and charged $18 for each scarf and $14 for each hat , then the system of equations which represents the constraints in this situation is s + h = 40 and 18s + 14h = 700 .
let the number of hats sold be = "h" ;
and let number of scarves sold be = "s" ;
the total number of scarves and hats sold are 40 ;
the situation is represented as : h + s = 40 ...equation(1) ;
the per unit cost for each scarf is = $18 ;
the per unit cost for each hat is = $14 ;
the amount for which the items are sold is = $700 ;
this situation is represented as : 18s + 14h = 700 ...equation(2) .
From equation(1) and equation(2) , we can conclude that ;
the system of equation to represent the situation is , s + h = 40 and 18s + 14h = 700 .
The given question is incomplete , the complete question is
The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat. If s represents the number of scarves sold and h represents the number of hats sold, write system of equations which represents the constraints in this situation ?
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Dax is buying coffee for 5 people in his office. He also leaves a $2:00 tip for the batista.
If his total,with tip,is $18.25 how much is each cup of coffee, not including the tip?
Enter your answers as a decimal like this:42.53
The cost of each cup of coffee, not including the tip, is $3.25.
What is division?One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.
Given:
Dax is buying coffee for 5 people in his office.
He also leaves a $2.00 tip for the Batista.
If his total, with tip, is $18.25,
then the total bill of the coffee,
= $18.25 - $2.00 (not including the tip)
= $16.25
The cost of one coffee is,
= $16.25 / 5
= $3.25.
Therefore, $3.25 is the cost of one coffee.
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a box contains 90 balls numbered from 1 to 90. if 8 balls are drawn with replacement, what is the probability that at least two of them have the same number?
The probability that at least two of the balls have the same number is 27.40%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
Probability requested is equivalent to:
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes
No. of ways to succeed = 90P8
No. of possible outcomes = 90^8
No. of ways to succeed =
nPr = n! / (n-r)!
90P8 = 90! / (90-8)!
90P8 = 90! / (82)!
90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!
90P8 = 90*89*88*87*86*85*84*83
90P8 = 3.13x10^15
P(no 2 have same number) = 3.13x10^15 / 90^8
P(no 2 have same number) = 0.73
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(at least 2 have same number) = 1 - 0.73
P(at least 2 have same number) = 0.2740 = 27.40%
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F(x)=(3x+5)^2-10
Please help
Answer:
Step-by-step explanation:
Vertex:
(
−
5
3
,
−
10
)
Focus:
(
−
5
3
,
−
359
36
)
Axis of Symmetry:
x
=
−
5
3
Directrix:
y
=
−
361
36
x
y
−
3
6
−
5
3
−
10
−
1
−
6
0
15
Answer: 9x^2-48x+54?
What is 1/2-(1/8+1/8)
Answer:
Hi, my name is Za'Riah! I will gladly help you with this problem. (see explanation)
Step-by-step explanation:
There really isn't much to explain or step out but here is the answer.
[tex]\frac{1}{2} - (\frac{1}{8}+ \frac{1}{8}) \\= \frac{1}{2} - \frac{1}{4} \\\\= \frac{1}{4}[/tex]
Find the measure of the indicated angle.
Answer:
Step-by-step explanation:
Given: ∠A =75°, ∠B=60° and ∠C=x
To find: ∠C
Proof: In △ABC
∠A =75° (given)
∠B=60° (given)
∠A+∠B +∠C=180° (angle sum property of a triangle: states that the sum of interior angles of a triangle is 180°)
75°+60°+∠C=180°
∠C=180-75+60
∠C=180-135°
∠C=45°
Therefore is 45 degrees.
What will be the length of the south, west and north side of the scale drawing?
Answer:
See below
Step-by-step explanation:
North, 50
West, 28
South, 71
Answer: i got North, 50
West, 28
South, 71
but have a good day
Step-by-step explanation:
Select the correct answer.
What is the value of x in the triangle?
10
O A. 10√2
OB. 10
O C. 20
OD. 20√2
Ο Ε.
10√3
10
Answer: A) 10√2
Step-by-step explanation:
You can find the value of x by using the Pythagorean Theorem.
a = 10
b = 10
c = x
a^2 + b^2 = c^2
(10)^2 + (10)^2 = c^2
100 + 100 = c^2
200 = c^2
Square root both sides.
c = √200
Simplify the square root. 100 x 2 is 200, and 100 is a perfect square.
√200 = √100√2
√100 can be simplified to 10. √2 can not be simplified.
The answer would be option A ) 10√2
The value of x in the given triangle is 10√2 units.
What is Pythagoras theorem?Pythagoras theorem states that in a right triangle the three sides are related by the formula, a²+b² = c², where c is the hypotenuse and a and b are the other two sides.
Given that, a triangle, we need to find the hypotenuse x,
Using the Pythagoras theorem,
10²+10² = x²
x² = 100 + 100
x² = 200
x = 10√2
Hence, the value of x in the given triangle is 10√2 units.
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How to find the value of x?
The answer is 56 degrees
The value of x from the triangle is x = 56°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the first triangle be represented as ABC
Let the second triangle be represented as ABD
Now , the measure of side ABD = x°
In the triangle ABC ,
∠ACB = 180° - 104° ( angles on a straight line = 180° )
So , the measure of ∠ACB = 76°
And , the measure of side ∠ACB = measure of side ∠ABC ( given )
So , the measure of side ∠ABC = 76°
And , for a triangle ∠A + ∠B + ∠C = 180°
Substituting the values in the equation , we get
The measure of ∠BAC = 180° - ( 76° + 76° )
The measure of ∠BAC = 28°
Now , the measure of ∠BAC + measure of ∠BAD = 90° ( given perpendicular line )
So , the measure of side ∠BAD = 90° - 28°
The measure of side ∠BAD = 62°
And , measure of side ∠BAD = measure of side ∠ABD ( given that they are similar )
So , the measure of side ∠ABD = 62°
And , for a triangle ∠A + ∠B + ∠D = 180°
Substituting the values in the equation , we get
The measure of side ABD = x° = 180° - ( 62° + 62° )
The measure of side ABD = x° = 180° - 124°
The measure of side ABD = x° = 56°
Hence , the measure of x is 56°
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Timmy buys four T-shirts costing t dollars. For buying four T-shirts he gets a 25% discount on each T-shirt. Write two expressions to represent the cost of the four T-shirts
Expression 1: 4t - (4t x 0.25) = 4t - (t) = 3t
Expression 2: 4 x (t - (t x 0.25)) = 4 x (t x 0.75) = 3t
where 't' is the cost of one T-shirt.
In expression 1, the original cost of the four T-shirts (4t) is multiplied by 25% (0.25) which is the given discount percent, and then subtracted from the original cost.
In expression 2, the original cost of one T-shirt (t) is multiplied by 25% (0.25) and subtracted from the original cost, and then the resulting cost (t x 0.75) is multiplied by four to represent the cost of four T-shirts.
Both expressions represent the cost of the four T-shirts after a 25% discount has been applied. they both yield the same result of 3t, which represents the final cost of the four T-shirts after the discount has been applied.
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5. Which of the following is parallel to the line y = 2/3x +5?
A.y=2/3x-4
B.y=2/3x-7
C.y=-2/3x+5
D.y=-2/3x+5
Answer:
To determine which of the given lines is parallel to the line y = 2/3x + 5, we need to compare their slopes. The slope of a line is the coefficient of the x variable, in this case 2/3.
The lines that are parallel have the same slope.
A.y=2/3x-4 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.
B.y=2/3x-7 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.
C.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.
D.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.
So the answer is A and B are parallel to the line y = 2/3x +5
3. George deposits
$500 in an account
that earns 2.5%
interest each year.
relative frequency distributions are generally more useful than frequency distributions when
Relative frequency distributions are generally more useful than frequency distributions when comparing identical-sized data sets.
Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.
It is possible to display the frequency distribution of data in a table or graph. Frequency tables, histograms, and bar charts are a few popular ways to display frequency distributions.
Tables of frequencies: A frequency table is an easy way to show how frequently a certain value or feature occurs.
Assume, for instance, that we have gathered information on height from a sample of 50 kids.
Both histograms and bar charts use columns drawn on a graph to visually represent frequencies.
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Complete answer is:-
Fill in the blanks -
Relative frequency distributions are generally more useful than frequency distributions when comparing data sets
what happens when the king of beasts runs in front of a train?
Answer: He dies.
Step-by-step explanation: A train is extremely powerful. It would kill on impact most of the time.
What is 5.81 X 8.7 X is multiplication please type how to do it not the right away answer I have to show work thank you
The multiplication of the numbers is 50.547.
What is the multiplication of numbers?When given two or more numbers to be multiplied, it is expected to get the product of the numbers. Such that an answer i.e. the final value which can either be a whole number or a number with a decimal part is gotten.
Given that 5.81 is to be multiplied by 8.7, we have;
One way to do it is by expressing the numbers in a standard form, so that we have;
5.81 X 8.7 = (581 x 10^-2) x (87 x 10^-1)
multiplying the whole parts of the number, we have;
581 x 87 = 50547
and multiplying the exponential part, we have;
10^-2 x 10^-1 = 10^-3
So that;
581 x 10^-2 x 87 x 10^-1 = 50547 x 10^-3
= 50.547
The multiplication gives 50.547.
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suppose you want to gamble in vegas. in a game, you win $x if the number is prime and lose $x/2 if composite. the number is uniformly randomly generated by a machine between 1 and 10 inclusive. will you play this game?
It is favorable to play this game.
This question requires a mathematical calculation of expected value to determine if the game is favorable or not.
The expected value is calculated as the sum of the product of each outcome and its corresponding probability.
The probability of winning $x for each prime number (2, 3, 5, 7) is 1/4, and the probability of losing $x/2 for each composite number (4, 6, 8, 9, 10) is 1/5.
Expected value = (1/4)*2x + (1/4)*3x + (1/4)*5x + (1/4)*7x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2
= (1/4)(2 + 3 + 5 + 7)x - (1/5)(x/2 + x + x/2 + x + x/2)
= (17/4)x - (5/2)x
= (17/4 - 5/2)x
= (3/4)x
Since the expected value is positive, it is favorable to play this game.
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What is the solution to the system of equations?
-1/2x+1/2y=-1
x-y=2
O There is no solution.
O There are infinitely many solutions.
O There is only one solution, (3, 1).
O There is only one solution, (-6,
The system of equations have no solution, the correct option is A.
What is a solution to a system of equations?For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
Given;
-1/2x+1/2y=-1 (1)
x-y=2 (2)
Now, multiplying equation 1 by 2
-x+y=-2
y=-2+x
Substituting the value of y in equation 2
x+2-x=2
Therefore, the equation have no solution.
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the length of a rectangular field is twice its breadth. Meghna jogged around it 5 times and covered a distance of 3 km. what is the length of the field
Answer:
Let x be the breadth of the rectangular field.
The length of the field is 2x.
We know that the perimeter of the rectangular field is (2x + 2x) = 4x.
Meghna jogged 5 times around the field, so she covered a distance of 4x km.
We know that 4x = 3km.
So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.
Answer:
Let x be the breadth of the rectangular field.
The length of the field is 2x.
We know that the perimeter of the rectangular field is (2x + 2x) = 4x.
Meghna jogged 5 times around the field, so she covered a distance of 4x km.
We know that 4x = 3km.
So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.
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Send your request via email on the company mail, include your name, employee ID number, and the W2 you are asking for the particular year.
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